Methods and systems for nucleic acid sequence analysis

ABSTRACT

Disclosed are new and improved methods and systems for nucleic acid sequence analysis that can analyze data indicative of natural by-products of nucleotide incorporation events without the need for exogenous labels or dyes to identify nucleic acid sequences of interest. In particular, the methods and systems of the present teachings can process such data and various forms thereof to align fragments of the nucleic acid(s) of interest, particularly those analyzed using an addition sequencing technique, for example, as occurs with the use of nucleotide flows.

RELATED APPLICATIONS

This application is related to U.S. Provisional Application No.61/438,432 filed Feb. 1, 2011, which is incorporated herein by referencein its entirety and U.S. Provisional Application No. 61/505,631 filedJul. 8, 2011, which is incorporated herein by reference in its entiretyand U.S. Provisional Application No. 61/530,830 filed Sep. 2, 2011,which is incorporated herein by reference in its entirety.

FIELD

The present teachings relate to data analysis. More particularly, thepresent teachings relate to nucleic acid sequence analysis.

BACKGROUND

Today, various instruments, apparatus, and systems generate largevolumes of data that require processing and analysis. Because a goal ofmany analytical techniques is high throughput and rapid analysis, notonly should the analytical instrument operate efficiently to generatedata, but the subsequent processing and analysis of the data also needsto be handled efficiently.

With respect to nucleic acid sequencing analysis, many known techniquesrely on the use of exogenous labels and dyes to identify or recognizethe incorporation of a nucleotide to a nucleic acid (polymer) or otherchemical entity. However, such techniques can suffer inaccuracies, forexample, where incorporation of a nucleotide with a label can besterically hindered and suffer incomplete or inefficient incorporation.Consequently, techniques have been developed that can detect the naturalby-products of transforming chemical reactions such as the incorporationof a natural nucleotide which produces a hydrogen ion. To that end, asequencing instrument that is capable of electronically detectingnucleotide incorporation resulting from extension of a nucleic acidstrand and can generate and output signals and data reflective of therelative hydrogen ion concentration associated with the nucleotideincorporation has been developed. See, e.g., U.S. patent applicationSer. Nos. 12/002,291, 12/474,897, and 12/492,844, each of which ishereby incorporated by reference in its entirety for all purposes.

Accordingly, there is a need for further data analysis methods andsystems that can efficiently process and analyze large volumes of datarelating to nucleic acid sequence analysis and more particularly, toalign or map nucleic acid fragments or sequences of various lengths.Further, there is a need for new data analysis methods and systems thatcan efficiently process data and signals indicative ofelectronically-detected chemical reactions, for example, nucleotideincorporation events, and transform these signals into other data andinformation, for example, base calls and nucleic acid sequenceinformation and reads, which then can be aligned, for example, against areference genome.

SUMMARY

In light of the foregoing, the present teachings provide new andimproved methods and systems for nucleic acid sequence analysis that canaddress and analyze data reflective of electronically-detected chemicaltargets and/or reaction by-products associated with nucleotideincorporation events without the need for exogenous labels or dyes tocharacterize nucleic acid sequences of interest. In various embodiments,the present teachings describe methods and systems that can process suchdata and various forms thereof including nucleotide flow orders to alignor map fragments of the nucleic acid(s) of interest. These methodologiesalso can be applied to conventional sequencing techniques and inparticular, sequencing by synthesis techniques.

In various embodiments, the present teachings describe a method ofaligning a putative nucleic acid sequence or fragment of a samplenucleic acid template or complement thereof against a candidatereference nucleic acid sequence. The method generally can includegenerating a putative nucleic acid sequence of a sample nucleic acidtemplate based on a series of nucleotide flows to a defined space andobtaining a series of signals from the defined space, where the samplenucleic acid template is associated with the defined space. The methodcan include identifying, based on the putative nucleic acid sequence, acandidate reference nucleic acid sequence to which the putative nucleicacid sequence may be aligned. The method can include forming, for atleast one base corresponding to the series of nucleotide flows, a matrixhaving two axes and a plurality of cells. Each cell can correspond to aspecific row and column of the two axes, where the matrix comprises afirst axis corresponding to the nucleobases of the candidate referencenucleic acid sequence and a second axis comprising a listing of thenumber (from 0 to n) of nucleobases in a homopolymer of the nucleobaseof the nucleotide flow. The method can include calculating the value ofeach cell of the matrix in response to the overlap of the nucleobase ofthe nucleotide flow with each nucleobase of the candidate referencenucleic acid sequence using a local sequence aligning method, forexample, a Smith-Waterman local sequence alignment algorithm. The methodalso can include weighting each value of the matrix in response to thesignal corresponding to one or more of the nucleobase of the nucleotideflow. The method can include tracing back through each of the matricesfor each of the nucleobases of the series of nucleotide flows todetermine the goodness of fit.

In various embodiments, the goodness of fit can be against the putativenucleic acid sequence. In other embodiments, the goodness of fit can beagainst the sample nucleic acid template. In certain embodiments, thegoodness of fit can be against both the putative nucleic acid sequenceand the sample nucleic acid template. In some embodiments, the methodcan include identifying more than one candidate reference nucleic acidsequence and the actions of forming, calculating, weighting and tracingdescribed above can be performed for the additional candidate referencenucleic acid sequences. In certain embodiments, the method can includecalculating an alignment score for each alignment against a differentcandidate reference nucleic acid sequence.

In various embodiments, each of the series of signals can berepresentative of the incorporation of nucleobases in a sample templatereflected for example as a change in hydrogen ion concentration in adefined space.

In certain embodiments, calculating the value of each cell of the matrixcan include scoring an alignment. In particular embodiments, scoring analignment can include setting a match parameter value, a non-matchparameter value, and a gap parameter value. In various embodiments thelocal sequence aligning method can include determining the maximum ofCell_(i-1,j-1)+a score, Cell_(i-1,j)+a first gap penalty, andCell_(i,j-1)+a second gap penalty.

In various embodiments, weighting can be performed by a function inresponse to the difference between a measured signal for a nucleobase ofthe series of nucleotide flows and an estimated value of thatnucleobase. In some embodiments, weighting can be performed by afunction in response to an approximated homopolymer number or length. Incertain embodiments the function can be determined as the absolute valueof the difference between the homopolymer number and the measured signalmultiplied by a calculated or predetermined penalty.

In particular embodiments, a method of aligning a putative nucleic acidsequence of a sample nucleic acid template or fragment against acandidate reference nucleic acid sequence can include forming a3-dimensional matrix having a plurality of cells, each cellcorresponding to a specific row and first and second columns of thethree axes, wherein the matrix can include a first axis corresponding tothe nucleobases of a candidate reference nucleic acid sequence, a secondaxis corresponding to a listing of the number (from 0 to n) ofnucleobases in a homopolymer of the nucleobase of the nucleotide flow,and a third axis corresponding to the nucleobases of a series ofnucleotide flows. The method also can include finding a desired or bestpath through the cells of the matrix to determine the goodness of fit ofthe candidate reference nucleic acid sequence, where the candidatereference nucleic acid sequence is identified based on a putativenucleic acid sequence and the putative nucleic acid sequence is based ona series of nucleotide flows to a defined space and a series of signalsfrom the defined space.

Numerous embodiments of the present teachings include a computer-useablemedium having computer readable instructions stored thereon forexecution by a processor to perform the various methods describedherein.

The methods also can include transmitting, displaying, storing, orprinting; or outputting to a user interface device, a computer readablestorage medium, a local computer system or a remote computer system,information related to one or more of the alignments and the informationassociated with the alignments, such as the sample nucleic acidtemplate, the signals, the defined space, the matrices, and equivalentsthereof.

The present teachings also include a computer-useable medium havingcomputer readable instructions stored thereon for execution by aprocessor to perform various embodiments of methods of the presentteachings. It should be understood that the signals described hereingenerally refer to non-transitory signals, for example, an electronicsignal, unless understood otherwise from the context of the discussion.

In various embodiments of systems of the present teachings for nucleicacid sequence analysis, a aligner module can be configured to practiceand/or carry out various methods of the present and/or teachings asdescribed herein and as understood by a skilled artisan.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not intended to limit the scope of the present teachings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present teachings described herein will be more fully understoodfrom the following description of various illustrative embodiments, whenread together with the accompanying drawings. It should be understoodthat the drawings described below are for illustration purposes only.The drawings are not necessarily to scale, with emphasis generally beingplaced on illustrating the principles of the present teachings. Thedrawings are not intended to limit the scope of the present teachings inany way.

FIG. 1 is a schematic diagram depicting an exemplary system for nucleicacid sequence analysis according to the present teachings.

FIG. 2 is a schematic diagram depicting an exemplary system forclassification according to the present teaching.

FIG. 3 is a schematic diagram depicting an exemplary structure where asample nucleic acid template, a sequencing key, and a primer sequenceare associated with a particle in accordance with the present teachings.

FIG. 4 is a schematic diagram depicting an exemplary process ofclassifying a well according to the present teachings.

FIG. 5 is a schematic diagram depicting an exemplary three-dimensionalmatrix for use in alignment methodologies of the present teachings.

FIG. 6 is a block diagram that illustrates a computer system, inaccordance with various embodiments.

FIG. 7 is a block diagram that illustrates a system for determining anucleic acid sequence, in accordance with various embodiments.

FIG. 8 is a graph illustrating the mapping sensitivity and false mappingrate.

DETAILED DESCRIPTION

Nucleic acid sequence analysis can be conducted using electronic sensorsthat generate signals indicative of enzymatic or chemical reactionsassociated with nucleotide incorporation events to provide anidentification of a sample nucleic acid sequence. More specifically, thepresent teachings provide methods and systems for the analysis ofsignals relating to consecutive base calls of fragments of a samplenucleic acid sequence of interest followed by the alignment of thefragments into a longer sample nucleic acid sequence. The methods caninclude transmitting, displaying, storing, printing, or outputtinginformation related to one or more parameters or variables of theanalysis, including equivalents thereof. The present teachings describemethods and systems that can accomplish such analyses through a varietyof different processing and analysis protocols, procedures, schemes, andassociated hardware.

Although the present teachings can have multiple, varied applications(including non-sequencing applications) and be used with data fromvarious analytical instruments, apparatus and systems, the presentteachings and description herein will be focused on data and signalsindicative or representative of changes in hydrogen ion concentration orpH, which can be associated with incorporation of a nucleotide into apolynucleotide, for example, a nucleic acid template strand. Such datacan be generated, for example, by Ion Torrent's Personal Genome Machine™(“PGM™”) or “Proton™”, available from Life Technologies Corporation(Carlsbad, Calif.), which is used as an exemplary analytical sequencinginstrument on which to focus the discussion herein. Consequently, itshould be understood that references herein to actions, structure andapparatus specific to the PGM/Proton will apply equally to more generalor generic actions, structure and apparatus, and vice versa, unlessindicated to the contrary. For example, references to a well shouldapply equally to a defined space, a reaction space, a reaction chamber,or an area; references to a chip should apply equally to areaction-permitting device or apparatus capable of association with anelectronic sensor detection apparatus, for example, ISFET, CMOS, orother sensors; and so on. However, it also should be understood that themethods and systems of the present teachings can be useful in otherapplications and should not be limited by the exemplary discussionherein. For example, the present teachings may be applied to othertechnologies including those which utilize fluorescent markets, labels,or [ ].

Throughout the application, where compositions are described as having,including, or comprising specific components, or where processes aredescribed as having, including, or comprising specific process steps, itis contemplated that compositions of the present teachings also consistessentially of, or consist of, the recited components, and that theprocesses of the present teachings also consist essentially of, orconsist of, the recited process steps.

In the application, where an element or component is said to be includedin and/or selected from a list of recited elements or components, itshould be understood that the element or component can be any one of therecited elements or components, or can be selected from a groupconsisting of two or more of the recited elements or components.Further, it should be understood that elements and/or features of acomposition, an apparatus, or a method described herein can be combinedin a variety of ways without departing from the spirit and scope of thepresent teachings, whether explicit or implicit herein.

The use of the terms “include,” “includes,” “including,” “have,” “has,”“having,” “contain,” “contains,” or “containing” should be generallyunderstood as open-ended and non-limiting unless specifically statedotherwise.

As used herein, “a” or “an” may also refer to “at least one” or “one ormore”. Further, unless expressly stated to the contrary, “or” refers toan inclusive- or and not to an exclusive- or. For example, a condition Aor B is satisfied by any one of the following: A is true (or present)and B is false (or not present), A is false (or not present) and B istrue (or present), and both A and B are true (or present).

The use of the singular herein includes the plural (and vice versa)unless specifically stated otherwise. In addition, where the use of theterm “about” is before a quantitative value, the present teachings alsoinclude the specific quantitative value itself, unless specificallystated otherwise. As used herein, the term “about” refers to a ±10%variation from the nominal value unless otherwise indicated or inferred.

As used herein, “nucleobases” can refer to the bases of a polynucleotidesequence, such as adenine (“A”), guanine (“G”), cytosine (“C”), uracil(“U”), or thymine (“T”). As used herein, “homopolymer” can refer to alength of polynucleotide sequence in which a nucleobase is repeated,such as “AAAA”.

As used herein, “nucleotide flow” can refer to a cycle or “flow” ofdeoxynucleoside triphosphate (“dNTP”) addition from which nucleotideincorporations may result.

At various places in the present specification, substituents aredisclosed in groups or in ranges. It is specifically intended that thedescription include each and every individual subcombination of themembers of such groups and ranges. By way of other examples, an integerin the range of 0 to 40 is specifically intended to individuallydisclose 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,36, 37, 38, 39, and 40, and an integer in the range of 1 to 20 isspecifically intended to individually disclose 1, 2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.

It should be understood that the order of steps or order for performingcertain actions is immaterial so long as the present teachings remainoperable. Moreover, two or more steps or actions can be conductedsimultaneously.

The present teachings provide methods and apparatus for analyzing data,for example, data and signals, resulting from label-free nucleic acid(e.g., deoxyribonucleic acid (“DNA”)) sequencing techniques, and inparticular, hydrogen ion producing and pH-based nucleic acid sequencingtechniques. Label-free nucleic acid sequencing techniques andinstruments, including methods for electronic detection of pH-basednucleic acid sequences, are described in Rothberg et al., U.S. PatentApplication Publication No. 2009/0026082 and other patent publicationscited herein.

Briefly, in pH-based nucleic acid sequencing, a nucleotide incorporationevent can be determined by measuring hydrogen ions that are generated orevolved as natural by-products of polymerase-catalyzed nucleotideextension reactions. In some embodiments, templates (e.g., fragments ofa nucleic acid sequence of interest) each having a primer and polymeraseoperably associated localized in reaction areas such as microwells,after which repeated cycles or “flows” of deoxynucleoside triphosphate(“dNTP”) addition and washing are carried out. In certain embodiments,such templates can comprise clonal populations and further may besecured to a solid support, such as a microparticle, bead, or the like(as used herein, generally, “particles”). In various embodiments, clonalpopulations affixed to beads or particles are loaded into reactionchambers. For example, templates can be prepared as disclosed in U.S.Patent Application Publication No. 2010/0304982 for sequencing andanalysis in the manner described herein.

In one exemplary approach, a primer can be annealed to a template sothat the primer's 3′ end can be extended by a polymerase wheneverappropriate dNTPs are available. The polymerase extends the primer byincorporating dNTPs when the next base in the template is the complementof the added dNTP. If there is one complementary base, there is expectedto be a single incorporation; if two, then two incorporations areexpected; if three, then three incorporations are expected; and so on.With each such incorporation, hydrogen ions are released, andcollectively a population of templates releasing hydrogen ions changesthe local pH of the reaction chamber.

The production of hydrogen ions is monotonically related to the numberof contiguous complementary bases in the template (as well as the totalnumber of template molecules with primer and polymerase that participatein an extension reaction). Thus, when there is a number of contiguouscomplementary bases of similar composition in the template, such as ahomopolymer region, the number of hydrogen ions generated, and thereforethe relative magnitude of the local pH change, is generally proportionalto the number of contiguous complementary bases. The correspondingoutput signals are sometimes referred to as “1-mer”, “2-mer”, “3-mer”output signals, and so on.

If the next base in the template is not complementary to the added orflowed dNTP, then no incorporation occurs and no hydrogen ion isgenerated or released (in which case, the output signal is sometimesreferred to as a “0-mer” output signal.) Between successive nucleotideadditions, a wash solution typically with a predetermined pH can be usedto remove residual dNTPs of the previous step in order to preventundesired misincorporations in later cycles, such as undesirablenucleotide carryover from one flow to another. In various embodiments,one of the different types of dNTPs is added sequentially to thereaction chambers so that each reaction chamber is exposed to the fourdifferent types of dNTPs, one at a time. Each exposure to a nucleotideoptionally followed by a washing step can be considered a “nucleotideflow.” Consecutive nucleotide flows can be considered a “cycle.” Forexample, a two cycle serial nucleotide flow order can be represented by:dATP, dCTP, dGTP, dTTP, dATP, dCTP, dGTP, dTTP, (or ACGTACGT) with eachexposure followed by a wash step.

Thus, based on the known nucleotide flow order to a reaction chamber andthe signals indicative of hydrogen ion concentration in the reactionchamber resulting from each nucleotide flow, the identity of the type,sequence and number of nucleotide(s) associated with a sample nucleicacid template present in the reaction chamber can be determined.Subsequently, where the sample nucleic acid templates include or arefragments of one or more sample nucleic acid sequences, the samplenucleic acid sequences (or at least portions thereof) can be determinedby aligning appropriately the sample nucleic acid templates, referencesequences, or to other sample fragment sequences.

To measure the hydrogen ions produced by a nucleotide incorporationevent in a particular reaction chamber, methods and apparatus that cancarry out and monitor a plurality of multi-step reactions withelectronic sensors can be used. For example, the electronic sensors canbe integrated into a sensor array suitable for simultaneously sensingindividual reactions taking place on or adjacent to or in sensingrelationship with a surface of an array. In some embodiments, an arrayof defined spaces or reaction areas can be integral with or coupled tosuch a sensor array.

The defined spaces and/or reaction spaces provide an area or a volumewhere a fluid or a solid can be confined, retained and/or localized. Thearea or the volume can be a predetermined area or a predeterminedvolume, for example, a depression a micro-machined well associated witha microwell plate, microtiter plate, microplate, or a chip ofsemiconductor material (a “semiconductor chip”), which chip can definethe reaction spaces or chambers such as wells. The area or the volume ofa defined space also can be determined based on the amount of fluid orsolid deposited on a substrate or in a volume otherwise defining adefined space. For example, isolated hydrophobic areas on a generallyhydrophobic surface can provide defined spaces. A defined space includesa reaction chamber, such as a well or a microwell.

An array of defined spaces can take the form of a microwell array or areaction chamber array made by conventional micro- or nanofabricationtechniques, for example, as described in Rothberg et al., U.S. PatentApplication Publication No. 2009/0127589; and Rothberg et al., U.K.Patent Application No. GB 24611127. In particular embodiments, eachmicrowell or reaction chamber in an array can be in a sensingrelationship, for example, electrical communication, with at least onesensor. In such an arrangement, one or more characteristics of theconditions in the microwell or reaction chamber can be detected ormeasured. The electronic sensors can convert changes in the presence,concentration or amounts of reaction by-products (or changes in ioniccharacter of the reactants) into an output signal, which can beregistered electronically, for example, as a change in a voltage levelor a current level which, in turn, can be processed to extractinformation about a chemical reaction or desired association event, forexample, a nucleotide incorporation event. Of course if no change occursin the defined space, then the output signal can remain relativelyconstant or no signal may be generated.

The sensors of the array can comprise at least one chemically sensitivefield effect transistor (“chemFET”) that can be configured to generateat least one output signal related to a property of a chemical reactionor target analyte of interest in proximity thereof. Such properties caninclude a concentration (or a change in concentration) of a reactant,product or by-product, or a value of physical property (or a change insuch value), such as ion concentration. Exemplary configurations andphysical characteristics of electronic sensor arrays and microwellarrays are described in U.S. Patent Application Publication Nos.2010/0304982 and 2009/0127589; and U.K. Patent Application No. GB24611127. In various embodiments, each of the electronic sensors of thearray can generate an output signal that depends in part on the value ofthe voltage of a reference electrode that is in fluid communication witha microwell array. In certain embodiments, a single reference electrodeconfiguration can be used so that each sensor generates an output signalwith the same reference voltage.

The initial measurement or interrogation of a defined space, forexample, a pH measurement can be represented as an electrical signal ora voltage, which also can be digitalized (e.g., a digital representationof the electrical signal or the voltage). Any of these measurements andrepresentations can be considered data or a signal.

Accordingly, in various embodiments, the methods of the presentteachings generally include generating and processing a series ofsignals indicative of the hydrogen ion concentration of a defined spaceor plurality of defined spaces such as an array of reaction wellsassociated with an array of sensors, where the defined space(s) comprisea sample nucleic acid template and associated enzymes and reagents usedin nucleotide incorporation. The method can include processing thegenerated signals to identify the type, number, and/or sequence ofnucleotides of the sample nucleic acid templates, thereby providing oneor more reads comprising consecutive base calls associated with thesample nucleic acid templates. The method also can include aligning thereads of a plurality of sample nucleic acid templates to determinelonger stretches of a sample nucleic acid sequence. The method furthercan include transmitting, displaying, storing, or printing; oroutputting to a user interface device, a computer readable storagemedium, a local computer system or a remote computer system, informationrelated to the analysis, which information can include data and signalsand results of the analysis of the data and signals. Such informationcan take the form of searchable and/or filterable lists of runs andreports, pictures, tables, charts, graphs, spreadsheets, correlations,sequences, and combinations thereof.

Systems of the present teachings include various hardware and componentsuseful to carry out various embodiments of the methods of the presentteachings. As shown in FIG. 1, a system 10 of the present teachingsgenerally can include a data processing module 12, a classificationmodule 14, a signal processing module 16, a base caller module 18, aread filter module 20, an alignment module 22, and a data output module24. Such a system or a variation thereof, can be set-up to be accessiblethrough a web-accessible data portal. In certain embodiments, themethods of the present teachings include the general steps associatedwith the modules shown in FIG. 1 such that the signals or data areprocessed from the data processing module to the data output module.Each of the components of the system and actions and features of methodsof the present teachings will be discussed in more detail below under anappropriate heading. It should be understood that the description ofembodiments the systems and associated actions can be applied equally tothe methods of the present teachings, and vice versa.

Data Processing Module

A data processing module generally is configured to receive data as aseries of signals, which can be reflective or indicative of a naturalby-product(s) of a transforming chemical reaction. For example, for thePGM, the signals are derived from nucleotide incorporation events (e.g.,incorporation of a dNTP associated with a sample nucleic acid template)by measuring hydrogen ions that are generated as natural by-products ofpolymerase-catalyzed nucleic acid extension reactions. Morespecifically, the hydrogen ion concentration (or pH) of a defined spacecan be measured repeatedly and at intervals timed to coincide with thenucleotide flows of different types of dNTPs to the defined space. Forthe PGM, the signals can represent a conversion of the pH value in eachwell into a voltage, which then can be converted into a digitalrepresentation of that voltage. While exemplified in the context ofelectronic detection of hydrogen ions released following a nucleotideincorporation event, it will be appreciated that the methods describedherein can be adapted for use with other sequencing approaches such assequencing by synthesis (SBS), and other electronic and non-electronicdetection techniques, such as those using fluorescent tags or labels.

More specifically, during a PGM run, for each nucleotide flow, anacquisition file may be generated. The acquisition file may contain thesignals from selected wells of a chip for the given nucleotide flow. Fora chip that contains about 1.5 million wells, each nucleotide flow canresult in about 1.5 million separate nucleotide sample incorporationevents. Following this through to its conclusion, for a series ofnucleotide flows or a series of resultant signals may be captured orsaved and reflect nucleotide incorporations over time.

A read can represent consecutive base calls associated with a sequenceof a nucleic acid. A read can reflect bases or base complementsassociated with a sample nucleic acid template, which can be associatedwith or present in a defined volume such as a well or associated with adefined area such as on a surface of a substrate. It should beunderstood that a read can include the full length sequence of thesample nucleic acid template or a portion thereof. A read can comprise asmall number of base calls, such as about eight nucleotides (base calls)but can contain larger numbers of base calls as well, such as 16 or morebase calls, 25 or more base calls, 50 or more base calls, 100 or morebase calls, or 120 or more nucleotides or base calls. The length of aread also can be expressed as a number of base pairs (bps) for one ormore sample templates.

The data processing module can perform multiple functions, includingreceiving or loading data, decompiling data, and offset correcting data.In various embodiments, the data processing module can receive signalsinto its memory, which signals can be temporarily or permanently stored.For example, the data or signals can stream off of an analyticalinstrument directly to the data processing module. Alternatively or incombination with direct steaming, the data processing module can accessor receive the data or signals after storage or collection on acomputer-readable medium such as a portable disk or hard drive. Duringthe receiving and/or storing, the signals can be compressed anddecompressed as desired.

In some embodiments, the methods can include operating in a dynamicframe rate compression mode whereby various portions of a nucleotideincorporation event or a nucleotide flow are captured at different framerates. The variable frame rate allows biologically specific events to becaptured with high resolution, while at the same time allowing theoverall file size to be decreased by allowing multiple frames to beaveraged where appropriate. A compression approach can use a key frameand/or delta compression technique whereby an initial value is stored,followed by the changes in that initial value, rather than storing theactual value each time. Such an approach can result in a nearly twotimes reduction in file size. Various embodiments of dynamic frame ratecompression are described in U.S. patent application Ser. No.13/339,846, filed Dec. 29, 2011 incorporated herein by reference.

In certain embodiments, the data processing module can perform signaloffset and/or background corrections. Signals can be stored using thevalues output by the analytical instrument. Each defined space can haveits own reference value. To compare defined space to defined space, thetwo defined spaces can use a common reference. The offset and/orbackground correction can take the average of the first few frameswithin each acquisition file and subtract that value from each definedspace, thus allowing measurements within the defined space to have acommon reference value.

In particular embodiments, the data processing module can perform pinneddefined space identification. Due to the nature of the output voltages,a range of values can exist for any given sensor array. For example,applying an instrument calibration can bring the majority of definedspaces within range of the hardware's analog-to-digital converters(“ADC”), some defined spaces can fall outside that range. The output canbe a distribution of values centered around the center voltage. Definedspaces or wells that reside outside a selected distribution can beconsidered “pinned” (functional defined spaces outside of the range ofthe ADC). In practice though, pinned wells or sample containment regionstypically represent a small percentage or fractional percentage of thetotal available sample processing areas associated with the sensorarray.

In various embodiments, the data processing module can flag or excludecertain defined spaces. Various flow cell configurations associated withthe sensor array make tradeoffs on flow velocity profiles and sensorarray coverage areas. For example, in certain sensor arrays, apercentage of the defined spaces can be covered or obscured by the flowcell components or packaging, or otherwise fluidically are inaccessibleor unaddressable. Consequently, a mask can be loaded, per chip type, tomark those defined spaces as excluded so as to avoid unnecessary and/orcomputationally inefficient down-stream processing of the sensor arrayand signals generated therefrom, where the information likely will beuninformative and/or unproductive.

In particular embodiments, the data processing module can receivedirectly acquisition files in DAT file format (e.g., acq_*.dat files),for example, streaming from an analytical instrument. In someembodiments, the data processing module can store, transmit or outputthe data, modified data, results and/or information in an appropriatedata file.

Classification Module

Because the data can include signals from thousands to millions ofindividual wells or sample containment regions, reducing the amount ofdata to be analyzed can increase efficiency and conserve file storagespace. Accordingly, sample regions of the sensor array can be classifiedas to whether the well generally contains useful information and shouldbe carried forward and included in the analysis, for example, using adefined space identification module. It should be understood that whilecertain data can be screened or otherwise modified, in practice mostdata usually is saved so that various screening and manipulating of thedata can be started anew, with different analysis protocol andparameters, if desired. Accordingly, not all embodiments of methods ofthe present teachings necessarily include each of the modules and/orsteps described herein.

In various embodiments, the classification module or classifying caninclude processing an array of wells in smaller regions rather than theentire array as one group. For example, a chip which contains an arrayof about 1.5 million wells can be segmented into 50×50 well regions,resulting in about 625 total regions. Such segregation can process manysmaller regions in parallel and takes advantage of, for example,parallel computing techniques, such as multi-core and/or multi-processcompute nodes that have such parallel computational capabilities.Regions in the chip that can contain fluidically similar wells can beprocessed similarly or together as smaller regions tend to be relativelyhomogeneous and allow comparison of wells to each other within a region.

In addition to reduction and segregation of the amount of data to beanalyzed, the classification module also can include identifying andparsing sample nucleic acid templates or fragments based on theirorigin, for example, with a sample nucleic acid template identificationmodule. That is, when using test nucleic acid fragments as a controland/or when pooling and sequencing fragmented samples of nucleic acidsfrom different origin (“multiplexing”), the test fragment and nucleicacid fragment sequences can be labeled or tagged prior to the sequencingprocess so that the resulting data can be appropriately analyzed. Tothis end, size-based and fluorescent tags can be used. Additionally, themethods and systems of the present teachings can use sequencing keys,e.g., a known nucleic acid sequence associated with a sample fragment,to identify and classify the resulting data and nucleic acid sequencinginformation.

Further, when a nucleic acid sequencing method uses sequencing keys asidentifiers of the nucleic acid fragments to which the sequencing keysare associated, a classification module can include a sequencing keysseparation module. That is, the sequencing keys should be designed to bereadily identified and separated such that the identification of a readbased on its sequencing key can be made with a certain level ofconfidence, for example, early in the data analysis process and/or basedon minimal amounts of data. Various embodiments of using sequencing keysare described in U.S. patent application Ser. No. 13/340,490, filed Dec.29, 2011 incorporated herein by reference.

In sum, as shown in FIG. 2, a classification module 14 can include adefined space identification module 142 and a sample nucleic acidtemplate identification module 144, both of which can process data fromsignals from defined spaces to evaluate, identify, flag, and/or excludeunuseful data while useful data can be processed further. Theclassification module 14 also can include a sequencing keys separationmodule 146, which can evaluate and determine the degree of separation orthe “orthogonality” of a pair of sequencing keys or bar codes.

However, first understanding the source of the contents of the wells canbe helpful. In some embodiments, when an array of wells is prepared foranalysis, fragments of a nucleic acid sequence of interest (e.g., samplenucleic acid templates) can be associated with a surface, for example,of a particle. Each sample nucleic acid template can be associated witha surface via covalent bonding or a specific binding or couplingreaction. A sample nucleic acid template can be derived from, forexample, a shot-gun fragmented DNA or amplicon library (which areexamples of library fragments), a sample emulsion PCR process creatingclonally-amplified sample nucleic acid templates on particles such asIonSphere™ particles.

A sequencing key can be associated with, such as added to the 5′ end,the sample nucleic acid template. In such a position, the sequencing keycan be near the beginning of a read to permit early identification andclassification of the sample nucleic acid template, for example, as atest or a library fragment or where no identification can be made, as anambiguous read or particle. Early classification can assist in reducingthe analysis time, for example, by determining whether usefulinformation is present and whether to exclude particular data fromfurther processing and analysis.

In addition to unknown nucleic acid fragments of interest and sequencingkeys, test nucleic acid sequence fragments (“test fragments”) having aknown nucleic acid sequence can be associated with particles. Testfragments often can be used as a reference and/or for quality control.Test fragments also can be considered examples of a sample nucleic acidtemplates.

To maintain the integrity of sample data from a well and its output, itcan be desirable to have only one fragment or nucleic acid sequence(including its clones or copies) associated with a single particle.Further, each well can be configured to contain a single particle (andthus, a single copy or population of copies of a single sample nucleicacid template can be associated with the well). The particles havinglibrary fragments and test fragments associated therewith then can beintroduced randomly into an array of wells on a chip. FIG. 3 shows anexemplary particle 50 associated with a sample nucleic acid template(non-bold nucleotides) 52, a sequencing key (bold nucleotides A G T C),and primer 56.

Moreover, although a well can contain a particle (e.g., not be an “emptywell” but a “particle-containing well”), the information obtained fromthe well can be unreliable due to no or low signal strength, ambiguousidentification of the sample nucleic acid template, and/or a particlewith more than one type of sample nucleic acid template or fragment(e.g., polyclonal). Consequently, a classification module generally isconfigured to determine the contents of each well.

FIG. 4 schematically shows an overview of an exemplary classification ofa well of a chip using signals from the well, for example, as can beaccomplished with a defined space identification module and a samplenucleic acid template identification module. Generally, a well 100 firstcan be determined to be a particle-containing well 102 or to be an emptywell 104 (one without a particle). The particle-containing well 102 canbe divided into a useful well 106 (one that provides useful information)and a non-informative well 108 (one that does not provide usefulinformation). Finally, using the sample nucleic acid templateidentification module, the useful well 106 can be divided into a wellcontaining test fragments 110, a well containing library fragments 112,or a well for which a determination cannot be made (ambiguous wells)114.

Although data typically is generated and measured and/or recorded fromeach well for each nucleotide flow, not all of the wells containparticles nor those wells with particles have nucleic acid sequences ofinterest or provide useful and reliable information. Accordingly, as afirst cut, data analysis can be narrowed to signals from wellscontaining a particle. If a well does not contain a particle, itgenerally will not provide useful information relating to a nucleotideincorporation event. Nevertheless, a well without a particle can beuseful for certain background readings and corrections and otherinformation relating to fluid flow and nucleotide flow(s) to the wells.

In certain embodiments, a known pH buffer at a different pH than thewash buffer can be distributed across the chip. The chip sensors candetect the pH change over time. Due to the diffusion rates on the wellsand the pH concentration, the change over time can be measured. Emptywells will generally have a different rate of pH change or equilibrationthan particle-containing wells due to the change in diffusion propertiesof those wells containing a particle. In particular embodiments, for agiven well, in order to determine whether the well contains a particleor is empty, the average of neighbor wells can be compared to the wellin question. If the diffusion rate in the well in question is slowerthan the average rate of surrounding neighbors, then this well can beconsidered to contain a particle. Otherwise the well can be identifiedas empty. Additional procedures to establish a baseline pH change overtime can include, for example, fitting the signal to exponentials orother models of the expected background signal.

At a next level, a particle-containing well may not produce a sufficientsignal or reading to be reliable (e.g., be a “dud particle”). Forexample, in particular embodiments, if a well does not produce asufficient signal over the first few to several key nucleotides (asdescribed below), such a well can be excluded from further analysis. Ingeneral, signals tend to be strongest and/or most consistent in theearly nucleotide flows of a sequence analysis. In addition, a samplenucleic acid template or fragment to be sequenced can have appended toit a known nucleic acid sequence or sequencing key, which can be used toidentify the origin of the sample nucleic acid template or fragment. Akey nucleotide can be a nucleotide that is present in such a sequencingkey. By evaluating the information obtained during the initialnucleotide flows, wells which do not conform to an expected signalstrength or sequence identification can be flagged or excluded fromfurther analysis. Such approaches as described herein can result inefficient data analysis because only wells with potentially usefulinformation are analyzed.

Sequencing Keys

In some embodiments, for particle-containing wells with a sufficientlystrong sequence and/or accurate signal (e.g., as determined byevaluating key nucleotide data), a sample nucleic acid templateidentification module within the classification module can determine ifthat particle is associated with fragments of a nucleic acid sequencefrom the library of interest (a “library particle”); with a test nucleicacid sequence fragment (a “test fragment particle”); or whether ameaningful distinction between a library and test fragment cannot bemade (an “ambiguous particle”).

In various embodiments, the identification of a particle as beingassociated with a library fragment or a test fragment can beaccomplished using sequencing keys and/or barcodes. In variousembodiments, the sequencing keys can be viewed as a unique identifier,such as a bar code, of the origin of the sample nucleic acid template orpopulation of nucleic acid fragments to permit appropriate sortingand/or association of nucleic acid sequences randomly dispersed in anarray. Certain approaches can use multiple sequencing keys. For example,where the nucleic acid sequences (fragments) in the wells have three ormore different origins (e.g., two original nucleic acid sequencepopulations of interest and a test fragment sequence), three or moresequencing keys or barcodes can be used to differentiate the origin ofeach fragment so as to allow later grouping of and/or sorting of thefragments based on the sequencing key or barcode appended thereto.

In an exemplary embodiment where two sequencing keys are used, onesequencing key can be a “library sequencing key,” for example, a knownartificial nucleic acid sequence identified or associated with afragment of a nucleic acid sequence from a library. The librarysequencing key can be associated with or be part of an adapter sequenceor have another association with the particles which include fragmentsfrom the library of a nucleic acid sequence of interest. The othersequencing key can be a “test fragment sequencing key,” for example, aknown artificial nucleic acid sequence identified or associated with aknown fragment of a nucleic acid used as a control or reference. If thelibrary sequencing key and the test fragment sequencing key are distinctidentifiers of each key, then a comparison of a read of unknown originagainst each of the library sequencing key and the test fragmentsequencing key should produce a match or a comparison of sufficientconfidence. If such identification cannot be made, then the informationfrom that well can be flagged, discarded, or ignored as being anambiguous well.

Depending on the format of the signals at the time of classification, acomparison of a sequencing key of a read to the reference sequencingkey(s) can be done in base-space format (e.g., using nucleotidedesignations such as A, C, G, and T). However, if the classification isdone at an earlier stage of data processing, the read may be not yet inbase-space format but can be in flow-space format (e.g., a series ofzeros and ones representing a nucleotide incorporation event (a one,“1”) or a non-incorporation event (a zero, “0”) for that particularnucleotide flow). (It should be understood that zeros and ones areconvenient representations of a non-incorporation event and a nucleotideincorporation event; however, any other symbol or designation could beused alternatively to represent and/or identify these events andnon-events). In certain embodiments, a homopolymer region can berepresented by a whole number greater than one rather than therespective number of one's in series. In flow-space format, thenucleotide flow order determines the flow-space format or flow ordervector.

For example, for a base-space sequence of “AT,” and a nucleotide floworder of “TACG,” the flow-space vector would be “0100X.” That is, thefirst nucleotide flow of “T” does not match the first nucleotide of thetemplate, such as, “A,” and would result in a non-incorporation event(“0”). The second nucleotide flow of “A” is a match and would result ina nucleotide incorporation event (“1”). The third nucleotide flow of “C”and the fourth nucleotide flow of “G” do not match the second nucleotideof the template, such as, “T,” and hence two consecutive zeros (“0, 0”)are added to the flow-space vector. The fifth nucleotide flow of “T” isa match and would result in a nucleotide incorporation event. However,because additional “T's” could present in the extended sample nucleicacid template (e.g., the extended nucleic acid template could be“ATTTG”), additional nucleotide incorporation events could occur duringthis fifth nucleotide flow. Consequently, an “X” is placed in theflow-space vector indicating a nucleotide incorporation event that mayhave been truncated.

Table 1 shows exemplary library and test fragment sequencing keys inboth base-space format and in flow-space format for a nucleotide floworder of TACG.

TABLE 1 Base-space format Flow-space format* Library Sequencing Key TCAG1010010X Test Fragment Sequencing ATCG 0100101X Key *based on nucleotideflow order TACG

Because the nucleotide flow order vector can be tested against eachsequencing key, the number of nucleotide flows required to sequence eachsequencing key can be determined. In particular embodiments, the lowernumber of nucleotide flows needed to sequence one of the sequencing keyscan be used for the comparison as that number of nucleotide flows shouldprovide sufficient information for separation.

Design of Sequencing Keys

In embodiments where sequencing keys are used to identify or separatenucleic acids of different origin, the sequencing keys should besufficiently distinguishable so that the identification can be made withconfidence. In some embodiments, the sequencing keys can be designed andcompared for their orthogonality (or distinctiveness). For example, invarious embodiments, each different nucleotide, such as A, C, G, and T,of the sequencing keys can be considered to be orthogonal if selectedconditions or rules are satisfied for a nucleotide pair in flow-space(e.g., considering G in the first sequencing key and G in the secondsequencing key).

Exemplary first condition: both a non-incorporation event (“0-mer”) anda nucleotide incorporation event (“1-mer”) are present in eachsequencing key for the nucleotide.

Exemplary second condition: for the first occurrence of the nucleotidein the first flow-space sequencing key, a nucleotide incorporation event(1-mer) occurs while during that nucleotide flow, a non-incorporationevent (0-mer) is present for the second sequencing key. In addition, thereverse is tested. That is, for the first occurrence of the nucleotidein the second flow-space sequencing key, a nucleotide incorporationevent (1-mer) occurs while during that nucleotide flow, anon-incorporation event (0-mer) is present for the first sequencing key.

If these conditions or conditions are satisfied, the nucleotide pair canbe considered to be orthogonal in flow-space for the two sequencingkeys. A separator event occurs when the nucleotide pairs are orthogonal.An increase in the number of separator events for two sequencing keysmeans in an increased separation of the two sequencing keys, whichincreased separation can result in increased confidence in the accuracyof the identification of the origin of the read of the sample nucleicacid template.

Sequencing keys of the present teachings based on flow-space formatvectors can permit the identification and classification of a samplenucleic acid template using less nucleotides than typically can berequired for state-of-the-art methods where comparisons usually are donein base-space format. That is, because sequencing keys can be designedusing nucleotide flow cycles and a particular nucleotide flow order tocreate orthogonality between or among the sequencing keys, a smallernumber of nucleotides can be required to provide a distinguishabledifference as to the origin of the sequence template.

The following examples of sequencing key design and evaluation oforthogonality are provided to illustrate further and to facilitate theunderstanding of the present teachings and are not in any way intendedto limit the invention.

Example 1

To evaluate the separation of the library key sequencing key and thetest fragment sequencing key in Table 1, the orthogonality of eachnucleotide is tested according to the above two described conditions.

First, the flow-space format vector of the library sequencing key (topline below) is aligned with the flow-space format vector of the testfragment sequencing key (bottom line below). In this depiction, each rowrepresents a sequencing key and each column represents a singlenucleotide flow.

1 0 1 0 0 1 0 0 1 0 0 1 0 1

In addition, the “X” is not included for each sequencing key as it is anunknown.

Next, to evaluate the T nucleotide, the T nucleotide flows areidentified, which in this example, correspond to the first and fifthnucleotide flows (for convenience, the numbers in the first and fifthcolumns are bolded and underlined below).

1 0 1 0 0 1 0 0 1 0 0 1 0 1

As can be seen in the above highlighted depiction, across each row(again, each row representing a sequencing key), a nucleotideincorporation event (bold, underlined “1”) and a non-incorporation event(bold, underlined “0”) occur for each sequencing key, thereby satisfyingthe first condition.

For the second condition, for each of the first and fifth columns(again, each column representing a single nucleotide flow), a nucleotideincorporation event (bold, underlined “1”) occurs for one sequencing keywhile during that same nucleotide flow (same column), anon-incorporation event (bold, underlined “0”) occurs for the othersequencing key. Consequently, because both conditions are satisfied,these two sequencing keys can be considered orthogonal for the Tnucleotide.

To evaluate the A nucleotide, the A nucleotide flows are identified,which in this example, correspond to the second and sixth nucleotideflows (for convenience, the numbers in the second and sixth columns arebolded and underlined below).

1 0 1 0 0 1 0 0 1 0 0 1 0 1

As can be seen in the above highlighted depiction, across each row, anucleotide incorporation event (bold, underlined “1”) and anon-incorporation event (bold, underlined “0”) occur for each sequencingkey, thereby satisfying the first condition.

For the second condition, for each of the second and sixth columns, anucleotide incorporation event (bold, underlined “1”) occurs for onesequencing key while during that same nucleotide flow, anon-incorporation event (bold, underlined “1”) occurs for the othersequencing key. Consequently, because both conditions are satisfied,these two sequencing keys can be considered orthogonal for the Anucleotide.

To evaluate the C nucleotide, the C nucleotide flows are identified,which in this example, correspond to the third and seventh nucleotideflows (for convenience, the numbers in the third and seventh columns arebolded and underlined below).

1 0 1 0 0 1 0 0 1 0 0 1 0 1

As can be seen in the above highlighted depiction, across each row, anucleotide incorporation event (bold, underlined “1”) and anon-incorporation event (bold, underlined “0”) occur for each sequencingkey, thereby satisfying the first condition.

For the second condition, for each of the third and seventh columns, anucleotide incorporation event (bold, underlined “1”) occurs for onesequencing key while during that same nucleotide flow, anon-incorporation event (bold, underlined “0”) occurs for the othersequencing key. Consequently, because both conditions are satisfied,these two sequencing keys can be considered orthogonal for the Cnucleotide.

To evaluate the G nucleotide, the G nucleotide flows are identified,which in this example, corresponds only to the fourth nucleotide flow(for convenience, the numbers in the fourth column are bolded andunderlined below).

1 0 1 0 0 1 0 0 1 0 0 1 0 1

Here, the first condition is not satisfied because a non-incorporationevent (bold, underlined “0”) occurs for both sequencing keys for thefirst G nucleotide flow. Accordingly, these two sequencing keys can beconsidered not orthogonal for the G nucleotide as a separation eventdoes not occur.

In sum, the library sequencing key and the test fragment sequencing keyin Table 1 can be considered orthogonal for three of the fournucleotides.

Example 2

In this example, an alternate library sequencing key is evaluatedagainst the test fragment sequencing key of Example 1. For these twosequencing keys, the orthogonality of each nucleotide is testedaccording to the above two described conditions.

The base-space format of the alternate library key is CTAG. For thenucleotide flow order of TACG, the corresponding flow-space formatvector is 00101101X.

Here, note that an additional nucleotide flow is needed to sequence thealternating library sequencing key (top row) than the test fragmentsequencing key (bottom row).

0 0 1 0 1 1 0 1 X 0 1 0 0 1 0 1 X

Accordingly, the number of nucleotide flows that can be used to evaluatethe separation or orthogonality of these two sequencing keys can bebased on the lowest number of nucleotide flows needed to sequence one ofthe sequencing keys. In this example, the alternate library sequencingkey can be sequenced in nine nucleotide flows whereas the test fragmentsequencing key can be sequenced in eight nucleotide flows. Because thelast base call, designated “X,” is unknown in each sequencing keybecause that position could represent the beginning of a homopolymer,the number of nucleotide flows that can be used for the alternatelibrary and the test fragment sequencing keys is eight and seven,respectively. Thus, the lowest number of known nucleotide flows betweenthe two sequencing keys is seven. Consequently, seven nucleotide flowscan be used to evaluate the number of separation events between the twosequencing keys.

Accordingly, similar to Example 1, the flow-space format vector of thefirst seven nucleotide flows of the alternate library sequencing key(top line below) first is aligned with the flow-space format vector ofthe first seven nucleotide flows of the test fragment sequencing key(bottom line below) As in Example 1, each row represents a sequencingkey and each column represents a single nucleotide flow.

0 0 1 0 1 1 0 0 1 0 0 1 0 1

To evaluate the T nucleotide, the T nucleotide flows are identified,which in this example, corresponds to the first and the fifth nucleotideflows (for convenience, the numbers in the first and the fifth columnsare bolded below).

0 0 1 0 1 1 0 0 1 0 0 1 0 1

Here, the first condition is not satisfied because a non-incorporationevent (bold “0”) occurs for both sequencing keys for the first Tnucleotide flow as well as a nucleotide incorporation event (bold “1”)occurs for both sequencing keys for the second T nucleotide flow.Accordingly, these two sequencing keys can be considered not orthogonalfor the T nucleotide as a separation event does not occur.

To evaluate the A nucleotide, the A nucleotide flows are identified,which in this example, correspond to the second and sixth nucleotideflows (for convenience, the numbers in the second and sixth columns arebolded below).

0 0 1 0 1 1 0 0 1 0 0 1 0 1

As can be seen in the above highlighted depiction, across each row, anucleotide incorporation event (bold “1”) and a non-incorporation event(bold “0”) occur for each sequencing key, thereby satisfying the firstcondition.

For the second condition, for each of the second and sixth columns, anucleotide incorporation event (bold “1”) occurs for one sequencing keywhile during that same nucleotide flow, a non-incorporation event (bold“0”) occurs for the other sequencing key. Consequently, because bothconditions are satisfied, these two sequencing keys can be consideredorthogonal for the A nucleotide.

To evaluate the C nucleotide, the C nucleotide flows are identified,which in this example, correspond to the third and seventh nucleotideflows (for convenience, the numbers in the third and seventh columns arebolded below).

0 0 1 0 1 1 0 0 1 0 0 1 0 1

As can be seen in the above highlighted depiction, across each row, anucleotide incorporation event (bold “1”) and a non-incorporation event(bold “0”) occur for each sequencing key, thereby satisfying the firstcondition.

For the second condition, for each of the third and seventh columns, anucleotide incorporation event (bold “1”) occurs for one sequencing keywhile during that same nucleotide flow, a non-incorporation event (bold“0”) occurs for the other sequencing key. Consequently, because bothconditions are satisfied, these two sequencing keys can be consideredorthogonal for the C nucleotide.

To evaluate the G nucleotide, the G nucleotide flows are identified,which in this example, corresponds only to the fourth nucleotide flow(for convenience, the numbers in the fourth column are bolded below).

0 0 1 0 1 1 0 0 1 0 0 1 0 1

Here, the first condition is not satisfied because a non-incorporationevent (bold “0”) occurs for both sequencing keys for the first Gnucleotide flow. Accordingly, these two sequencing keys can beconsidered not orthogonal for the G nucleotide as a separation eventdoes not occur.

In sum, the alternate library sequencing key and the test fragmentsequencing key can be considered orthogonal for two of the fournucleotides, which separation is not as large as the library sequencingkey and the test fragment sequencing key in Example 1.

It should be understood that in some embodiments, the nucleotide floworder can be altered. The only change will be the flow-space formatvector to accommodate the alternate nucleotide flow order. Therefore,for any nucleotide flow order, flow-space format vectors can be createdfrom the base call sequences (base-space format) to compare theorthogonality of the nucleotides as described and illustrated herein.

In particular embodiments, the classification module can receivedirectly a data file. The classification module can store transmit, oroutput classification information in a MASK file format (e.g.,bfmask.bin), which can contain bit flags for each well, indicating thecontents of each well.

Signal Processing Module

A signal processing module generally is configured to analyze signalinformation from a defined space and an associated sample nucleic acidtemplate being sequenced. The signal processing module can output anincorporation signal. The signal processing module can use informationand data resulting from the classification module and methods describedtherein, but also can use data or signals.

Several potential sources of noise can affect output signals fromsensors when a large number (e.g., tens or hundreds of thousands ormillions) of electrochemical reactions are carried out over an array ofdefined spaces. The data and signals received by the signal processingmodule can include background information that can be excluded inanalyzing the initial signal and generating an incorporation signal.

In some embodiments, the signal processing module can focus only ondefined spaces containing particles and/or those defined spacesproducing a sufficiently strong signal to indicate a nucleotideincorporation event (e.g., in FIG. 1, useful wells 106). Anincorporation signal indicates a nucleotide incorporation event becauseof the hydrogen ion concentration or pH of a defined space during aparticular nucleotide flow. However, during a nucleotide incorporationevent, a measured signal can have additional components, referred to asbackground or noise. The background or noise portion of the signal canbe present during each flow and can vary over time, across an array ofwells, and during an acquisition. For example, the changing pH above aseries of wells can introduce a background measurement variance.Accordingly, a measured background signal can be filtered based on thewell and particle properties.

In certain embodiments, the signal processing module can create anincorporation fitting model. In some embodiments, the incorporationfitting model has two parts. The first part can derive the backgroundsignal that would have been measured in a given defined space had nonucleotide incorporation event occurred. The second part can involvesubtracting (or fitting) the background signal from the signal and thenexamining and analyzing (or fitting to) the signal that remains. Theresult of the incorporation fitting model can be an estimate ofincorporation during each nucleotide flow for each well.

In particular embodiments, a signal processing module can receive dataacquired from the sequencing reactions. The signal processing module canstore, transmit and/or output incorporation signals and relatedinformation and data in specified file format. The signal processingmodule can further output an incorporation signal per defined space, perflow.

Base Caller Module

A base caller module generally is configured to transform anincorporation signal into a base call and compile consecutive base callsassociated with a sample nucleic acid template into a read. A base callrefers to a particular nucleotide, for example, dATP (“A”), dCTP (“C”),dGTP (“G”), or dTTP (“T”). The base caller module can perform one ormore signal normalizations, signal phase and signal droop (e.g., enzymeefficiency loss) estimations, signal corrections, and identify orestimate base calls for each flow of each defined space. The base callermodule can share, transmit or output non-incorporation events as well asincorporation events.

In some embodiments, a read can be normalized. Normalization initiallycan use the data and signals from the signal processing module. Usingknown expected 1-mer events (e.g., identified with the sequencing keys),a 1-mer average signal initially can be established. As the base callermodule processes each defined space, additional base calls can beaccurately determined and additional measurements then can be used tore-normalize the signals. The re-normalization process can gain a higherconfidence (e.g., a higher signal-to-noise ratio) of the signal fromeach defined space.

In certain embodiments, observed signal droop can be attributed to DNApolymerase loss that can occur during a sequencing run. Such DNApolymerase loss usually is experienced only during nucleotideincorporation events, with values typically in the range of about 0.1%to about 0.2% over the course of a run. By averaging groups of reads ina region together and/or averaging their signals after normalization, anexponential can be fit to the resulting curve, from which the rate ofsignal loss over time can be extracted. Consequently, an estimate of theDNA polymerase loss during nucleotide incorporation events can bedetermined.

In particular embodiments, after the signal droop has been established,the signal droop can be used in a signal phase model as a constant for aread. Signal estimates can vary across an array of defined spaces, butsignal droop estimates often can be assumed to be fixed for eachprocessed region. The signal phase model then can fit the carry-forwardand incomplete extension parameters for a read, over a limited number ofand excluding certain nucleotide flows. The output from this fit can bean estimate of the carry-forward and incomplete extension for eachdefined space. The values can be averaged over small regions to reduceerrors and noise in the fit. The output carry-forward and incompleteextension values can be used as inputs to other parts of the base callermodule, for example, a solver function.

In various embodiments, a solver function of the base caller module canapply the phase and droop estimates to the normalized signals and makepredictions of the likely signal measurements for each nucleotide flowfor probable nucleotide incorporation events. The solver function cancompare the actual measured value to a list of predicted values. Thebest fit prediction at each nucleotide flow then can be used as the basecall for that flow. For example, a 0-mer, 1-mer, 2-mer, 3-mer, 4-mer,and higher order nucleotide incorporations can be predicted at eachnucleotide flow. The solver function can continue such processing overthe entire read. At the end of one pass, a good estimate of all basecalls for that read can be made. The solver function then can iterateover the read again, applying the same phase and droop estimates at eachnucleotide flow, to refine the base calls. Thus, knowledge of futurebases in later nucleotide flows can be included in the model to moreaccurately account for carry-forward or incomplete extension effects.

In particular embodiments, a base caller module can receive data inspecified file format and can store, transmit or output reads andrelated information in a standard flowgram format (for example, “SFF”).

Read Filter Module

A read filter module generally is configured to generate quality metricsfor each base call of a read and for each read of a set of reads tofacilitate filtering out of low quality or uninformative reads and basecalls. The identification and removal of low quality or uncertain basecalls and reads can improve the efficiency and accuracy of the analysisand results. In particular, low quality base calls can be removed fromthe output data by filtering out entire reads and/or trimming lowquality 3′ ends of reads using a variety of filters and protocols. Forexample, the quality of a read can be improved by trimming an adaptersequence at the end of the read. These operations typically are appliedas post-processing operations after the initial base calls have beenestimated.

Quality Score Determination

Overall in some embodiments, a per base quality score can be assigned toeach base call of a read, and the per base quality score can be writtento a file along with the read itself. A per base quality score can beassigned by calculating quality metrics for the base call(s) and/or theread. The quality metrics can be analyzed individually or in combinationby comparison to a pre-defined quality look-up table (a phred-liketable) established through prior system training. The quality metricscan include estimates of accuracy of the current base call, thenucleotide flow, and earlier or later base calls and/or nucleotide flowsfor each read.

More specifically, a quality score module generally is configured toinclude a phred-like per base quality look-up table and a trainingsystem to generate the quality look-up table. Phred quality scores werefirst created by the program Phred to aid in sequencing nucleic acid(DNA) in the Human Genome Project. Phred quality scores can characterizethe quality of a DNA sequence. In the present teachings, based onnucleotide flow values for each base, several quality predictors can becalculated for each base call of a read. These quality predictors can beused as part of an index to look-up an appropriate quality score for thebase call in the phred-like quality look-up table.

In some embodiments, a quality look-up table can be generated byselecting a representative data set to use as a training set. Thetraining set can use a variety of quality predictors to characterize thequality of a base call. In an exemplary embodiment, multiple qualitypredictors are used to capture what are believed to be the majority offeatures that can correlate with an indicated quality. The qualitypredictors can include, but are not limited to, base position, localnoise, read noise, multiple incorporations, phase error, and environmentnoise.

The base position quality predictor can be the base position in the readfrom the start of the nucleic acid sequence.

The local noise quality predictor can be the noise in an immediateneighborhood of a given base. The immediate neighborhood can be varieddepending on the particulars of the application and run. For example,the local noise quality predictor can be defined to be within plus orminus (±) one base of the given base. However, other definitions of animmediate neighborhood can be used in the analysis, for example, within±2 bases of the given base.

The read noise quality predictor can be a peak-normalized expression ofthe mean and the standard deviation of all 0-mers and 1-mers of a read.

In the case of multiple incorporations of the same nucleotide in onenucleotide flow (a homopolymer region), the multiple incorporationsquality predictor can assign to the last base in the homopolymer regiona value equivalent to the total number of incorporations during thatparticular nucleotide flow while all other bases in the homopolymerregion can be assigned a value of 1.

The phase error quality predictor can be the number of incorporations ofthe same nucleotide in the previous nucleotide flow.

The environment noise quality predictor can be the noise in a largerneighborhood of a given base. As with the local noise quality predictor,the area of the larger neighborhood can vary depending on theapplication and run. For example, the environmental noise qualitypredictor can be in a larger neighborhood which is defined to be within±10 bases of the given base. However, the larger neighborhood can bedefined to be within ±5 bases, ±6 bases, ±7 bases, ±8 bases, ±9 bases,±11 bases, ±12 bases, or more.

As already mentioned, the quality predictors can be calculated from thenucleotide flow values for each base. Also using aligned reads, thequality score module can establish the various quality predictors, alongwith whether or not a base was called correctly to create a vector. Thisvector can be used as the input into a training system. In variousembodiments, the quality predictors can be binned, and an extensive listof all combinations with their empirical quality score can be recorded.An algorithm can be used to summarize quality predictor values thatcorrespond to the same quality and to select a representative subset ofthese combinations.

The output of the training and selection algorithm can be a (phred-like)quality look-up table in which each quality predictor can be part of anindex in the table. Consequently, the established quality look-up tablecan be used to look up the phred-like per base quality score for aparticular base call.

In certain embodiments, after a quality look-up table is generated, thequality look-up table can be used to assign a per base quality scoreindependent of alignment. For example, the six quality predictors can becalculated for each base of a sample nucleic acid sequence template. Thecorresponding per base quality score can be determined by locating, inthe quality look-up table, the first line for which all six calculatedquality predictors are less than or equal to the quality predictorvalues in the quality look-up table. The quality score then can be readfrom the same line.

Filtering Reads

Overall in various embodiments, the read filtering module or filteringof reads can include calculating an overall quality metric representingthe base caller module's ability to correct accurately and base call thesignal measurements. Low quality reads can be mixed reads, poor signalquality reads, or very low copy-count reads that produce low qualitynucleic acid information and sequences such that they do not fit theexpected incorporation model. Reads identified as low quality typicallyare excluded and not written to the SFF or FASTQ file.

Various types of read filtering can occur. For example, read filteringcan include targeted removal of reads that are derived from wells withnon-clonal nucleic acid template populations and/or targeted removal ofreads that are generally a poor fit to the base calling model'sexpectations for high quality data, whether because of low or poorsignal quality from the well or a low copy count of sample nucleic acidtemplates.

More specifically, identified non-clonal nucleic acidtemplate-containing particles or wells typically are filtered from thedata as they contain a mixture of different nucleic acid templates. Thatis, a mixed nucleic acid template read can result from nucleic acidtemplates that are amplified on a single particle but are derived frommultiple, different input nucleic acid templates. A mixed nucleic acidtemplate read can occur because of the presence of two or more distinctnucleic acid fragments in the vesicle at the start of the emulsion PCRstage, or because of the collapsing together of different emulsionvesicles.

Regardless of their origin, mixed nucleic acid template reads usuallycan be identified by searching for reads in which an unusually largeproportion of nucleotide flows are estimated to result in a nucleotideincorporation event. For example, when no mixed nucleic acid templatereads exist, each particle will have a single sample nucleic acidtemplate species amplified onto it. Based on a four-nucleobase flowcycle and uniform and random nucleotide content in the sample nucleicacid sequence template, sequencing of such a sample nucleic acidtemplate is expected to result in approximately one-half (50%) of thenucleotide flows having a positive nucleotide incorporation event. Incontrast, when a particle contains multiple different sample nucleicacid templates, or mixed nucleic acid template reads, the number ofnucleotide flows in which a positive nucleotide incorporation eventsignal can be expected to increase substantially.

In particular embodiments, the percentage of positive flows (“PPF”)(such as, the percentage of positive nucleotide incorporation eventsbased on the total number of nucleotide flows) can be evaluated over agiven number of nucleotide flows, for example, the first 30 nucleotideflows, the first 40 nucleotide flows, the first 60 nucleotide flows, orthe first 75 nucleotide flows. Subsequently, a PPF threshold can be setto exclude reads having a PPF greater than the threshold value. Forexample, in certain embodiments, if the PPF value is greater than about60%, or greater than about 65% or greater than about 70%, the read canbe excluded from the set of reads for further analysis, for example,alignment, and/or before writing out to an SFF or FASTQ file. It shouldbe understood that where a particular read does not have the minimumnumber of nucleotide flows to meet the nucleotide flow number threshold,the actual number of nucleotide flows can be used to calculate the PPFand determine whether to filter the read.

In addition, certain reads can have a PPF that is below the expectedvalue, which also can result in such a read being filtered. Thus, invarious embodiments of the present methods, a read can be identified asacceptable if the read has a PPF between about 40% to about 60%, betweenabout 45% to about 55%, between about 35% to about 65%, and betweenabout 30% to about 70%, including various combinations of upper andlower thresholds as dictated by the particular application and run.

In some embodiments, test fragments can be excluded from read filteringbased on the PPF. Test fragment sequences often are designed withsequences that typically do not occur naturally and therefore, canresult in a large PPF. Accordingly, the methods of the present teachingspermit the identification of such test fragments but do not filter thecorresponding reads from a set of filtered reads.

It should be understood that in some limited embodiments, it is possiblefor the methods of the present teachings to filter from furtherprocessing certain possibly useful nucleic acid sequences using the PPFfilter. For example, a long sample nucleic acid template which has arepeating sequence that is exactly the same as the nucleotide flow order(e.g., TACG) would be expected to have a positive nucleotideincorporation event for every nucleotide flow (theoretically, a PPF of100%). Because of the large PPF, the hypothetical, long sample nucleicacid template would be identified as a mixed nucleic acid template readand filtered. Although such a piece of information may be unused orunder-utilized, in practice, such sequences should be very rare and thebenefits of generally excluding low quality reads resulting from mixednucleic acid templates based on a threshold PPF are favored overexcluding a very small proportion of genuine reads.

As for other criteria for read filtering, in various embodiments, readfiltering can include targeted removal of reads that are generally apoor fit to the base calling model's expectations for high quality data.A typical or “well-behaved” read can be modeled and will have certainexpectations about its signal distribution. For example, after theamount of incomplete extension (“IE”) and carry forward (“CF”) phasingeffects have been estimated, certain expectations are present for howsignals in neighboring nucleotide flows should be elevated or depressed.For example, when a positive IE is in effect, a large homopolymersequence should result in a depressed signal in the nucleotide flowcorresponding to the homopolymer while an elevated signal should bepresent in the next nucleotide flow of the same nucleotide.

In some embodiments, an observed signal can be compared to an expectedsignal based on a prediction of a base calling model for each nucleotideflow for each read. The difference between the observed signal and thepredicted signal can be referred to as the flow residual for the welland nucleotide flow in question (e.g., flow residual equals observedsignal minus predicted signal). In general, a high quality read which iswell-described by the base calling model and the nucleic acid sequencethat it estimates should have a low residual value.

More particularly, in certain embodiments, the median absolute value ofthe flow residual values over a number of initial nucleotide flows canbe tracked for each read as a measure of the agreement between theobserved data and the base calling model. If the median absolute flowresidual value of a read is greater than a predefined threshold, thenthe read can be considered unreliable and it can be filtered andexcluded from further processing. For example, in particularembodiments, the median absolute flow residual value can be determinedover the first 30 nucleotide flows, the first 40 nucleotide flows, thefirst 50 nucleotide flows, the first 60 nucleotide flows or the first 70nucleotide flows. In some embodiments, if the median absolute flowresidual value is above a threshold of about 0.1, about 0.12, about0.13, about 0.15, or about 0.2, or greater, the read can be filteredfrom the set of reads. For these criteria, a median absolute flowresidual value filter can be applied to reads of both library fragmentsand test-fragments.

In addition to the above, other characteristics of reads can beidentified and evaluated to determine whether the read should befiltered as being of low quality. For example, the strength of thesignal from a particular well can be evaluated over the first two,three, or four key nucleotides. A key nucleotide can be a nucleotidethat is present in a library sequencing key or a test fragmentsequencing key. For wells that do not produce a strong signal acrosseach of the predetermined number of (key) nucleotides, the readresulting from that well can be filtered.

For various embodiments, a read can be required to contain a minimumnumber (threshold) of base calls (nucleotides) to avoid identificationas a low quality read. For example, a threshold read length can be atleast 6 bases, at least 8 bases, at least 10 bases, at least 12 bases,at least 15 bases, at least 20 bases, or at least 25 bases, or more. Ifa read does not contain the threshold read length, the read can befiltered from the set of reads for further processing.

Further, in certain embodiments where sequencing keys are used, a readfilter can require an exact match of a sequence of the read to thecorresponding library sequencing key for that run. If an exact match isnot identified, the read can be filtered.

Trimming Base Calls

In various embodiments, rather than filtering a read in its entirety, aread can be trimmed, such as having one or more nucleotides (base calls)excised or removed from the read, until an acceptable level of qualitypersists for the remaining portion of the read, which can be used infurther processing and/or written to a SFF or FASTQ file. For example, aread that contains an adapter sequence (e.g., a B-adapter) can betrimmed to remove the adapter sequence (base calls) as well as any otherbase calls determined to be of low quality. Read trimming usually occursat the 3′ end of a read. However, in certain embodiments, base calls atthe 5′ end of a read can be trimmed, for example, where the base callscorrespond to a sequencing key such as a library sequencing key.

As with other filters, each read trimming filter independently can beapplied and the resulting, trimmed read length used in furtherprocessing or written to an appropriate file can be the sequence withthe shortest length, which should contain only high quality base callsbased on the filtering criteria. If the resulting trimmed read length isshorter than the threshold read length (as discussed above in connectionwith read filtering), the read can be filtered out entirely.

In various embodiments, a read can be examined to determine if anadapter (sequence) or a portion thereof can be identified with highconfidence within a read. If a sequence matching an adapter sequence isfound, the read can be trimmed to the base call (nucleotide) immediatelyprior to the start of the adapter.

In particular embodiments, searching a read for a match to a knownadapter sequence can be done in flow-space using flow-space vectors.More specifically, the effects of CF and IE can be reversed to produce aphase-corrected ionogram (which can be stored in a SFF file). If a readextends into the adapter sequence, the 3′ end of the phase-correctedionogram can exhibit a pattern that is characteristic of the adaptersequence. In some embodiments, the method includes testing each positionof the phase-corrected ionogram to determine whether it matches thepattern expected for the adapter sequence. Testing can include computingthe Euclidean distance between the phase-corrected ionogram at the testposition and the known ionogram for the adapter. If the distance fallsbelow an adapter ionogram distance threshold, the corresponding position(translated from flow-space format back to base-space format) can bemarked and/or recorded as an adapter trim location. If the distance doesnot fall below the adapter ionogram distance threshold, that position ofthe read does not match to the adapter sequence. In particularembodiments, the adapter ionogram distance threshold is a Euclideandistance of 5. However, depending on the application, the adapterionogram distance threshold can be a distance of 2, 3, 4, 6, 7, 8, 9, ormore.

In certain embodiments, lower quality base calls at the 3′ end of a readcan be trimmed. Considering the distribution of per base quality scoreswithin a read, the highest quality base calls tend to occur at the startof the read, where phase errors typically are the smallest in magnitude.For a read that contains low quality base calls before reaching the endof a sequence of a sample nucleic acid template, the lower quality basecalls at the 3′ end can be trimmed. The trimming of low quality basecalls at the 3′ end of a read can performed using a per base qualityscore threshold.

In particular embodiments, base call trimming using a per base qualityscore can include scanning along the base calls of a read and computinga moving average in a fixed-length base call window along the read. Aread trim point can be set to trim the earliest (5′-most) base call atwhich the moving average of the per base quality score drops below amoving average base quality score threshold. In certain embodiments, thebase call window size is 30 base calls and the moving average basequality score threshold, below which trimming will occur, is a qualityscore of nine. Of course, depending upon the particular run andapplication, the window size can be five base calls, 10 base calls, 15base calls, 20 base calls, 25 base calls, 35 base calls, or 40 basecalls, or more. The moving average base quality score threshold also canvary depending on many factors and can be a quality score of 5, 6, 7, 8,10, 11, 12, 13, 14, or 15, or more.

In particular embodiments, a read filter module can receive an SFF file.The read filter module can store, transmit and/or output trimmed readsand/or a filtered set of reads, and related data and information (forexample, for each read, an adapter marker, a sequence key, and/orthreshold and quality markers such as per base quality scores,indications of cuts to the reads, and/or the thresholds used in analysisof the data) in SFF or FASTQ file format as well as in a SequenceAlignment/Map (“SAM”) file.

Alignment Module

An alignment module or aligner generally is configured to align thereads of a plurality of sample nucleic acid templates to determine alonger portion of a sample nucleic acid sequence. Although the overallgoal typically is to identity the longer portion of the sample nucleicacid sequence, a first step usually is the identification of the nucleicacid sequences of sample nucleic acid templates or fragments (reads) inthe wells. Reads may be assembled using the BFAST aligner or the TorrentMapping Alignment Program (“TMAP”) aligner, which can be usedspecifically with data and signals generated using nucleotide flowmethodologies.

The aligner can accept as inputs some or all of the reads, for example,a set of filtered reads received from the read filter module. Thealigner also can input and/or use a reference genome and index files tofacilitate alignment and/or to control quality.

With respect to nucleotide flow methodologies and as discussed herein,the nucleotide flow order and the strength of the respective signal fromeach nucleotide flow can generate a putative nucleic acid sequence orread for the particular sample nucleic acid template in a well fromwhich the signals were generated. However, because nucleic acidsequencing technologies can create relatively short reads of from ten toa few hundred bases in length, alignment of such reads in a practicaltime, especially when considering a complete genome, is a significantchallenge. Accordingly, methods and algorithms can be used that reducethe size or complexity of the search target for aligning a particularread. For example, a read or putative nucleic acid sequence (also knownas a query sequence or query nucleic acid sequence) can be passedthrough an index of a reference genome or alternatively, by indexing thereads and searching a reference genome. As a result of indexing,candidate alignment locations (“CALs”) or candidate mapping locations(“CMLs”) can be identified and used to perform local alignment analyses.In certain embodiments, the CAL or CML can be referred to a candidatereference nucleic acid sequence, which can be useful in determining thesequence of the sample nucleic acid template.

In some embodiments, more than one algorithm can be used to identify acandidate reference nucleic acid sequence. Algorithms that can be usedin connection with the present teachings include, but are not limitedto, Burrows-Wheeler Aligner (“BWA”)-short (Li and Durbin, Bioinformatics25, 14:1754-1760 (2009)), BWA-long (Li and Durbin, Bioinformatics 26,5:589-595 (2010)), and Sequence Search and Alignment by HashingAlgorithm (“SSAHA”) (Ning, Cox and Mullikin, Genome Research 11,10:1725-1729 (2001)). In various embodiments, to take advantage of thestrengths of each algorithm, two of the three or all three of thesealgorithms can be used in an alignment strategy to identify a list of atleast one, or one or more, candidate reference nucleic acid sequences.For example, BWA-short quickly can map near-perfect reads while BMA-longand the SSAHA variant can sensitively map less similar and longer reads.Of course, other relevant algorithms can be used instead or tosupplement the ones specifically mentioned.

In various embodiments, reads not mapped in a first stage can be mappedwith a new set of algorithms and parameters in a second stage. Incertain embodiments, the second stage uses the same algorithm(s) as thefirst stage, but with different parameters. In such circumstances, atwo-stage mapping or alignment process can permit the majority of readsto be mapped or aligned with a fast set of algorithms and parameterswhile leaving difficult to map or align reads for a second round, whichcan use more sensitive algorithms and parameters.

After a candidate reference nucleic acid sequence is identified, it canbe aligned against the putative nucleic acid sequence using a localsequence aligning method, for example, a Smith-Waterman algorithm (see,e.g., Smith and Waterman, Journal of Molecular Biology 147 (10:195-197(1981)). The resulting alignments can be aggregated to determine thebest mapping(s) or goodness of fit.

In some embodiments and with particular reference to data relating tonucleotide flow methodologies, a challenge exists to avoid miscallinghomopolymer lengths as insertion and deletion (“indels”) errors canoccur during alignment and post-processing. For example, when the signalfrom one nucleotide flow falls between the values for one nucleotideincorporation event and two nucleotide incorporation events, it isuncertain whether the putative nucleic acid sequence should include oneor two of the nucleobases in its sequence. A Smith-Waterman algorithm asdescribed above normally cannot account for such homopolymerdifferences. To address this problem, the present teachings providemethods and systems where a putative nucleic acid sequence and acandidate reference nucleic acid sequence can be aligned using a thirddimension.

More specifically, a three-dimensional matrix can be formed by using aSmith-Waterman algorithm to create a two-dimensional matrix where oneaxis is the nucleobases of the candidate reference nucleic acid sequenceand the other axis is the length of the homopolymer or homopolymernumber (e.g., “L” as used in the example below). That is, to account forall possible homopolymers during a single nucleotide flow, an alignmentstrategy can be implemented that accounts for all or at least areasonable number of homopolymers lengths, where L equals zero means nonucleobase present (a non-incorporation event for that nucleotide flow),L equals one means one nucleobase is present (one nucleotideincorporation event occurred), L equals two means that two of thenucleobases in that particular nucleotide flow were incorporated, and soon. Accordingly, in some embodiments, a matrix can be created in whichthe length of the homopolymer on one axis is from zero to three, fromzero to five, from zero to seven, from zero to ten, and so on with anyreasonable number of homopolymer length as a variable.

As is familiar with a Smith-Waterman algorithm, various scores areattributed to different occurrences and overlaps of the nucleobasesbeing compared. For example, the scores can include a match score or amatch parameter value, a non-match score or a non-match parameter value,and a gap score or gap parameter value. The non-match score and the gapscore can be negative values as they can be considered penalties. Otherscores and parameters can be used depending on the particularapplication. For example, a flow penalty can be used to weight values inthe matrices. Moreover, while the same scores and parameters can be usedin name, the values of these scores and parameters can vary depending onthe particular application and other variables.

Finally, the third dimension across which the above-describedtwo-dimensional matrix is created and extended is the nucleotide floworder. That is, for a particular nucleotide flow, the above-describedtwo-dimensional Smith-Waterman algorithm is created using the particularnucleobase of the nucleotide flow as the parameter against which todetermine whether a match or mismatch occurred with respect to eachnucleobase of the candidate reference nucleic acid sequence. In otherwords, for a first nucleotide flow, a two-dimensional matrix can begenerated using a Smith-Waterman algorithm where the axes are L=0-10 andthe specific nucleobases of the candidate reference nucleic acidsequence. Next, for a second nucleotide flow, another two-dimensionalmatrix can be generated using the Smith-Waterman algorithm where theaxes remain as L=0-10 and the specific nucleobases of the candidatereference nucleic acid sequence. However, the second nucleotide flowlikely will be of a different nucleotide such that the analysis andvalues in the cells of the matrix will vary as the comparison againstthe candidate reference nucleic acid sequence will be different.

FIG. 5 depicts a three-dimensional axes system where each of theparameters discussed above can be visualized as creating athree-dimensional matrix having cells corresponding to the valuesdetermined by a Smith-Waterman algorithm. Visualized another way, thethree-dimensional matrix can be viewed as stacked Smith-Watermanmatrices.

After such a three-dimensional matrix is generated, methods of thepresent teachings include tracing back through each of thetwo-dimensional matrices for each of the nucleobases of the series ofnucleotide flows to determine a goodness of fit. That is, similar to themovement through a Smith-Waterman matrix from one corner to theopposite, diagonal corner to determine an alignment fit, a trajectory istraced from one corner of the three-dimensional matrix to the opposite,diagonal corner. In certain embodiments, the goodness of fit isdetermined against the putative nucleic acid sequence. In particularembodiments, the goodness of fit is determined against the samplenucleic acid template. In some embodiments, the goodness of fit isdetermined against both the putative nucleic acid sequence and thesample nucleic acid template.

In various embodiments, after creating a two-dimensional matrix ofhomopolymer number and the nucleobases of the candidate referencenucleic acid sequence, the values in the cells can be weighted inresponse to the signal of the nucleobase of the nucleotide flow. Thatis, to account for the various lengths of homopolymer stretches that maybe present in a putative nucleic acid sequence, the value of thehomopolymer length can vary greatly, for example, from L=0-10. However,if the signal from a particular nucleotide flow is near zero, thelikelihood that a non-incorporation event occurred is high. Accordingly,as the value of L becomes larger, it is less likely that the nucleobasewas incorporated multiple times. Therefore, a weighting function can beused to account for such deviation from the observed signal.

In various embodiments, the generation of the matrices can be simplifiedby using information from the immediately prior matrix so as to collapsesome of the data together. For example, after a first matrix of thenucleobases of a candidate reference nucleic acid sequence versushomopolymer number is generated for a first nucleotide flow, the highestnumber in each column (corresponding to the nucleobases) can be used asthe top row (corresponding to L=0) in the matrix for a second nucleotideflow, and so on.

In some embodiments, more than one candidate reference nucleic acidsequence is identified. In such circumstances, the alignment analysiscan be done against each of the candidate reference nucleic acidsequences. Each analysis can provide an alignment score, which can beindicative of goodness of fit to each of the candidate reference nucleicacid sequences thereby providing the most likely match or alignment ofthe putative nucleic acid sequence and/or the sample nucleic acidtemplate. An alignment score can be the score of the cell or cells wherethe tracing or backtracking through the matrix or matrices begins, whichscore can include the sum of all or a portion of the cells through whichthe trajectory leads.

The following example is for illustration purposes only and should beconsidered non-limiting. However, the following example can be useful inunderstanding the specifics of the alignment methodologies describedherein.

Example 3

For the purposes of this example, the nucleotide flow order is:

ACTGACTGAand the respective signals generated by a well after each nucleotideflow are:

-   -   0.1, 0.3, 0.2, 1.4, 0.3, 1.2, 0.8, 1.5, 0.7.

Based on the nucleotide flow sequence, a putative nucleic acid sequenceis generated using the signals rounded to the nearest integer (as eithera nucleotide incorporation event occurred or did not occur, but notpartially). Thus, the above nucleotide flow order and signals establisha putative nucleic acid sequence as follows:

FLOW SEQUENCE PUTATIVE SEQUENCE A 0.1 C 0.3 T 0.2 G 1.4 → G A 0.3 C 1.2→ C T 0.8 → T G 1.5 → G A 0.7 → A

In sum, the putative nucleic acid sequence (with associated signal inparentheses) becomes: G (1.4), C (1.2), T (0.8), G (1.5), and A (0.7),or GCTGA (without the signal values).

For the purpose of this example, assume that the candidate referencenucleic acid sequence is identified to be: GCTGGA.

First, the degree of fit or goodness of fit between each of the putativenucleotides of the read and the nucleotides of the candidate referencenucleic acid sequence is determined using a Smith-Waterman algorithm inwhich the value of a given cell in the matrix (e.g., Cell_(i,j)) is:

(Cell_(i,j))=maximum of:

Cell_(i-1,j-1)+score

or

Cell_(i-1,j)+gap penalty

or

Cell_(i,j-1)+gap penalty,

where i is in the direction of the candidate reference nucleic acidsequence (across in this example) and j is in the direction of theputative nucleic acid sequence (down in this example).

The score is determined by whether a given nucleotide of the putativenucleic acid sequence is a match or a mismatch to the correspondingnucleotide of the candidate reference nucleic acid sequence asdetermined by which cell of the matrix is being considered. Further, anevaluation against an adjacent vertical cell (Cell_(i,j-1)) is given agap penalty of −7 and an evaluation against an adjacent horizontal cell(Cell_(i-1,j)) is given a gap penalty of −7. Finally a flow penalty,which will be described later, is given a value of −5.

A matrix first is formed with the candidate reference nucleic acidsequence to be examined along the top and the putative nucleic acidsequence down the side.

G C T G G A (reference) (putative) G C T G A

First, because the alignment is of the full sequences, multiples of thegap penalties (−7) for each entry in the first row and each entry in thefirst column are set. Each row entry is designated (S) because the entrycorresponds to a start position.

G C T G G A (reference)    0 (S) −7 (S) −14 (S) −21 (S) −28 (S) −35 (S)−42 (S) (putative) G  −7 (S)

C −14 (S) T −21 (S) G −28 (S) A −35 (S)

Moving from left to right, the first cell (shown as an empty box above)is evaluated for (putative-G) against (reference-G). As the cells arefilled in, a letter after the value indicates from where the value wasderived. For example, an M (match or mismatch) indicates the value wasderived from the diagonally adjacent cell; a D (deletion) indicates thatthe value was derived from the adjacent horizontal cell; and an I(insertion) indicates that the value was derived from the adjacentvertical cell. The letters are useful as they can guide a path ortrajectory back through the matrix.

First, looking at the diagonally adjacent cell, up and to the left:

Cell_(i-1,j-1)+score=0 (for the Cell_(i-1,j-1))+5 (for match of putativeG to reference G)=5.

Next looking to the horizontal cell to the left:

Cell_(i-1,j)+gap penalty=−7 (for Cell_(i-1,j))−7=−14.

Next looking to the vertical cell above:

Cell_(i,j-1)+gap penalty=−7 (for Cell_(i,j-1))−7=−14.

Thus the maximum of these three calculations is 5, so the value ofCell_(i,j)=5. An M is placed after the value to indicate that the valuewas derived from the diagonally adjacent cell.

G C T G G A i→    0 (S) −7 (S) −14 (S) −21 (S) −28 (S) −35 (S) −42 (S)

G  −7 (S)

C −14 (S) T −21 (S) G −28 (S) A −35 (S)

The next cell (indicated by the empty box below) is (putative-C) against(reference-G).

G C T G G A i→    0 (S) −7 (S) −14 (S) −21 (S) −28 (S) −35 (S) −42 (S)

G  −7 (S)   5 (M) C −14 (S)

T −21 (S) G −28 (S) A −35 (S)

To find its value, again calculate the value by evaluating the diagonalcell:

Cell_(i-1,j-1)+score=−7 (for Cell_(i-1,j-1))+(−4 mismatch of putative-Cand reference-G)=−11.

Calculating the value against the adjacent horizontal cell:

Cell_(i-1,j)+gap penalty=−14 (Cell_(i-1,j))−7 (gap penalty)=−21.

Finally looking at the adjacent vertical cell:

Cell_(i,j-1)+gap penalty=5 (Cell_(i,j-1))−7 (gap penalty)=−2.

So the value of the cell is −2 and it has an I after it because thevalue was derived from the adjacent vertical cell.

G C T G G A i→    0 (S) −7 (S) −14 (S) −21 (S) −28 (S) −35 (S) −42 (S)

G  −7 (S)   5 (M) C −14 (S)

T −21 (S) G −28 (S) A −35 (S)

Continuing to move down the first column (reference-G), the next cell,indicated by the box, is:

G C T G G A i→   0 (S) -7 (S) -14 (S) -21 (S) -28 (S) -35 (S) -42 (S) G -7 (S)  5 (M)   0 C -14 (S) -2 (I) T -21 (S)

G -28 (S)

A -35 (S)

This cell is (putative-A) evaluated against (reference-G). For thiscell, the algorithm yields:

Cell_(i-1,j-1)+score=−14 (for Cell_(i-1,j-1))+(−4 mismatch of(putative-A) and (reference-G)=−18.

Cell_(i-1,j)+gap penalty=−21 (Cell_(i-1,j))−7 (gap penalty)=−28.

Cell_(i,j-1)+gap=−2 (Cell_(i,j-1))−7 (gap penalty)=−9.

So the value of the cell is −9 and the value has an I after it as thevalue was derived from the adjacent vertical cell.

Proceeding down the column in the same manner, the complete column forthe first reference-G looks like:

G C T G G A i→ 0 (S) −7 (S) −14 (S) −21 (S) −28 (S) −35 (S) −42 (S) G −7(S) 5 (M) 0 C −14 (S) −2 (I) T −21 (S) −9 (I) G −28 (S) −16 (M)

A −35 (S) −23 (I)

The next column is reference-C, with the first cell against putative-G.

G C T G G A i→   0 (S)  -7 (S) -14 (S) -21 (S) -28 (S) -35 (S) -42 (S) G -7 (S)   5 (M)

C -14 (S)  -2 (I) T -21 (S)  -9 (I) G -28 (S) -16 (M)

A -35 (S) -23 (I)

Because putative-G and reference-C do not match, the score is −4.Looking at the diagonally adjacent cell, Cell_(i,j), becomes:Cell_(i-1,j-1)+score=−7+−4=−11.

Looking next at the horizontal and vertical cells:

Cell_(i-1,j)+gap penalty=5−7=−2

Cell_(i,j-1)+gap penalty=−14−7=−21

The maximum of the three calculations is −2 and therefore, the cellvalue is −2, with a D after it to indicate that the value was derivedfrom the adjacent horizontal cell.

G C T G G A i→ 0 (S) −7 (S) −14 (S) −21 (S) −28 (S) −35 (S) −42 (S) G −7(S) 5 (M) −2 (D) C −14 (S) −2 (I) T −21 (S) −9 (I) G −28 (S) −16 (M)

A −35 (S) −23 (I)

Next looking at the cell for putative-C and reference-C shown in theblock below:

G C T G G A i→   0 (S)  -7 (S) -14 (S) -21 (S) -28 (S) -35 (S) -42 (S) G -7 (S)   5 (M)  -2 (D) C -14 (S)  -2 (I)

T -21 (S)  -9 (I) G -28 (S) -16 (M)

A -35 (S) -23 (I)

Because putative-C and reference-C match, the score is 5. Looking at thediagonally adjacent cell, the Cell_(i,j) becomes:

Cell_(i-1,j-1)+score=5+5=10

Looking next at the horizontal and vertical cells:

Cell_(i-1,j)+gap penalty=−2−7=−9

Cell_(i,j-1)+gap penalty=−2−7=−9

The maximum of the three calculations is 10 and therefore, the cellvalue is 10, with an M after it to indicate that the value was derivedfrom the diagonally adjacent cell.

G C T G G A i→ 0 (S) −7 (S) −14 (S) −21 (S) −28 (S) −35 (S) −42 (S) G −7(S) 5 (M) −2 (D) C −14 (S) −2 (I) 10 (M) T −21 (S) −9 (I) G −28 (S) −16(M)

A −35 (S) −23 (I)

The next cell in the next column has reference-T against=putative-G:

G C T G G A i→   0 (S)  -7 (S) -14 (S) -21 (S) -28 (S) -35 (S) -42 (S) G -7 (S)   5 (M)  -2 (D)

C -14 (S)  -2 (I) 10 (M) T -21 (S)  -9 (I) G -28 (S) -16 (M)

A -35 (S) -23 (I)

Cell_(i-1,j-1)+score=−14−4=−18

Cell_(i-1,j)+gap=−2−7=−9

Cell_(i,j-1)+gap=−21−7=−28

Consequently, this cell becomes −9 (D).

G C T G G A i→ 0 (S) −7 (S) −14 (S) −21 (S) −28 (S) −35 (S) −42 (S) G −7(S) 5 (M) −2 (D) −9 (D) C −14 (S) −2 (I) 10 (M) T −21 (S) −9 (I) G −28(S) −16 (M)

A −35 (S) −23 (I)

Looking at the next cell down:

G C T G G A i→   0 (S)  -7 (S) -14 (S) -21 (S) -28 (S) -35 (S) -42 (S) G -7 (S)   5 (M)  -2 (D)  -9 (D) C -14 (S)  -2 (I)  10 (M)

T -21 (S)  -9 (I) G -28 (S) -16 (M)

A -35 (S) -23 (I)

Cell_(i-1,j-1)+score=−2−4=−6

Cell_(i-1,j)+gap=10−7=3

Cell_(i,j-1)+gap=−9−7=−16

Consequently, this cell is 3 (D).

G C T G G A i→ 0 (S) −7 (S) −14 (S) −21 (S) −28 (S) −35 (S) −42 (S) G −7(S) 5 (M) −2 (D) −9 (D) C −14 (S) −2 (I) 10 (M) 3 (D) T −21 (S) −9 (I) G−28 (S) −16 (M)

A −35 (S) −23 (I)

In sum, each iteration of the analysis method or algorithm looks at:

1) the immediate preceding value on the diagonal and adds theappropriate score;

2) the value in the immediate proceeding vertical cell and adds the gappenalty;

3) the value in the immediate preceding horizontal cell and adds the gappenalty; and from these values, the most positive calculated value forthe cell is used.

Doing this for the rest of the matrix results in:

G C T G G A i→ 0 (S) −7 (S) −14 (S) −21 (S) −28 (S) −35 (S) −42 (S) G −7(S) 5 (M) −2 (D) −9 (D) −16 (M) 23 (M) −30 (D) C −14 (S) −2 (I) 10 (M) 3(D) −4 (D) −11 (D) −18 (D) T −21 (S) −9 (I) 3 (I) 15 (M) 8 (D) 1 (D) −6(D) G −28 (S) −16 (M) −4 (I) 8 (I) 20 (M) 13 (M) 6 (D)

A −35 (S) −23 (I) −11 (I) 1 (I) 13 (I) 16 (M) 18 (M)

Next, to determine the alignment, a trajectory is traced back throughthe matrix working column-by-column, with the starting point being thecell with the highest value in the far right hand column. A path then istraced to the left using the letter designation to determine thedirection of movement, such as left, diagonal, or up.

Here, the highest value in the far right column is 18 (M), which is amatch of A. The M means that the next cell is the diagonally adjacentcell, which is 13 (M), a match for G. The M means that the next cellagain is the diagonally adjacent cell, which is 8 (D). Here, no match isfound but a deletion so that the sequence gets a dash and currently is:-G A.

Next, the D means that the next cell is the adjacent horizontal cell,which is 15 (M), a match for T. The M means that the next cell is thediagonally adjacent cell, which is 10 (M), a match for C. The M meansthat the next cell again is the diagonally adjacent cell, which is 5(M), a match for G. Finally, the M again means that the next cell is thediagonally adjacent cell, which is 0 (S), the start cell. Consequently,the alignment using a Smith-Waterman algorithm provides the sequence: GC T-G A.

Thus, based on the Smith-Waterman algorithm, it is unclear whether adeletion is present in the putative nucleic acid sequence or ahomopolymer stretch was miscalled.

Using an embodiment of an algorithm of the present teachings, a matrixof the candidate reference nucleic acid sequence is compared against thehomopolymer number (“L”) for each nucleotide of the nucleotide floworder thereby creating a three-dimensional matrix. For this example, Lis set from zero to three to keep the example reasonable.

First, multiples of the gap penalties (−7) for each entry in the firstrow and each entry in the first column are set. Each row entry isdesignated (D) because the entry corresponds to a deletion and eachcolumn entry is designated (I) because the entry corresponds to aninsertion. The number after the letter in parentheses indicates thehomopolymer row in which it is located, for example, a zero indicatesthat its associated value is in the L=0 row of homopolymers.

G C T G G A L = 0 0 −7 (D0) −14 (D0) −21 (D0) −28 (D0) −35 (D0) −42 (D0)L = 1 −7 (I) L = 2 −14 (I) L = 3 −21 (I)

The first nucleotide in the nucleotide flow sequence is (A), which has asignal value of (0.1). The flow order nucleotide (A) is not a match forthe candidate reference nucleic acid sequence nucleotide (G). Using theSmith-Waterman technique as described above, the first cell (shown asthe box below) is given a score of −4 because of the mismatch.

A = 0.1 G C T G G A L = 0   0 -7 (D0) -14 (D0) -21 (D0) -28 (D0) -35(D0) -42 (D0) L = 1  -7 (I)

L = 2 -14 (I) L = 3 -21 (I)

As a result, −4 is added to the adjacent diagonal cell above (0) and theCell_(i,j) becomes:

Cell_(i-1,j-1)+score=0−4=−4

Cell_(i-1,j)+gap penalty=−7−7=−14

Cell_(i-1,j-1)+gap penalty=−7−7=−14

Accordingly, the value for the cell is −4, with an (M) designation forits origin.

A = 0.1 G C T G G A L = 0 0 −7 (D0) −14 (D0) −21 (D0) −28 (D0) −35 (D0)−42 (D0) L = 1 −7 (I) −4 (M) L = 2 −14 (I) L = 3 −21 (I)

The next cell (shown by the box below) is assessed by comparing the flownucleotide (A) again against the reference (G). Again there is no matchso the score is −4 again.

A = 0.1 G C T G G A L = 0   0 -7 (D0) -14 (D0) -21 (D0) -28 (D0) -35(D0) -42 (D0) L = 1  -7 (I) -4 (M)

L = 2 -14 (I) L = 3 -21 (I)

Cell_(i-1,j-1)+score=−7 (diagonal cell)−4 (mismatch score)=−11

Cell_(i-1,j)+gap penalty=−4 (horizontal cell)−7 (gap penalty)=−11

Cell_(i,j-1)+gap penalty=−14 (vertical cell)−7 (gap penalty)=−21

So the cell is given a value of −11(M), due to the mismatch.

G C T G G A L = 0   0 -7 (D0) -14 (D0) -21 (D0) -28 (D0) -35 (D0) -42(D0) L = 1  -7 (I) -4 (M)

L = 2 -14 (I) L = 3 -21 (I)

Continuing for the next cell:

A = 0.1 G C T G G A L = 0   0 -7 (D0) -14 (D0) -21 (D0) -28 (D0) -35(D0) -42 (D0) L = 1  -7 (I) -4 (M) -11 (M)

L = 2 -14 (I) L = 3 -21 (I)

Cell_(i-1,j-1)+score=−14 (diagonal cell)−4 (mismatch score)=−18

Cell_(i-1,j)+gap penalty=−11 (horizontal cell)−7 (gap penalty)=−18

Cell_(i,j-1)+gap penalty=−21 (vertical cell)−7 (gap penalty)=−28

Consequently, the cell has a value of −18 (M) (note that an M wasdesignated rather than a D).

A = 0.1 G C T G G A L = 0   0 -7 (D0) -14 (D0) -21 (D0) -28 (D0) -35(D0) -42 (D0) L = 1  -7 (I) -4 (M) -11 (M)

L = 2 -14 (I) L = 3 -21 (I)

Continuing this way for the remaining entries, the matrix becomes:

A = 0.1 G C T G G A L = 0 0 −7 (D0) −14 (D0) −21 (D0) −28 (D0) −35 (D0)−42 (D0) L = 1 −7 (I) −4 (M) −11 (M) −18 (M) −25 (M) −32 (M) −30 (M) L =2 −14 (I) −11 (M) −8 (M) −15 (M) −22 (M) −29 (M) −27 (M) L = 3 −21 (I)−18 (M) −15 (M) −12 (M) −19 (M) −26 (M) −24 (M)

Next each value is weighted by a function which takes into account howfar the signal value (here A=0.1) is from the expected value (A=0). Thefunction that is used should give the same number whether the signal isgreater than or less than the putative value. The function also shouldtake into account the fact that a homopolymer of length 3 is moreunlikely than a homopolymer of length 2.

In one embodiment the weight factor is WF=abs(L-signal value)*flowpenalty (wherein flow penalty=−5). So for L=0,WF=−abs(0−0.1)*(−5)=(−0.5) for each element in the table. Ignoring everyother cell in the matrix except row L=0, the weighting factor −0.5 isadded to each value in the L=0 row. The matrix row for L=0 then becomes(shown in grey):

Repeating this for L=1, the weight factor becomesWF=−abs(1−0.1)*(−5)=(−4.5). Applying this to each entry in the L=1 row,the matrix becomes:

G C T G G A L = 0 −0.5 (S0) −7.5 (D0) −14.5 (D0) −21.5 (D0) −28.5 (D0)−35.5 (D0) −42.5 (D0) L = 1 −11.5 (I) −8.5 (M) −15.5 (M) −22.5 (M) −29.5(M) −36.5 (M) −34.5 (M) L = 2 −14 (I) −11 (M) −8 (M) −15 (M) −22 (M) −29(M) −27 (M) L = 3 −21 (I) −18 (M) −15 (M) −12 (M) −19 (M) −26 (M) −24(M)

Doing this for L=2 and L=3, the WF=−abs(2−0.1)*(−5)=(−9.5) andWF=−abs(3−0.1)*(−5)=(−14.5), respectively, the weighted matrix becomes:

A = 0.1 G C T G G A L = 0 −0.5 (S0) −7.5 (D0) −14.5 (D0) −21.5 (D0)−28.5 (D0) −35.5 (D0) −42.5 (D0) L = 1 −11.5 (I) −8.5 (M) −15.5 (M)−22.5 (M) −29.5 (M) −36.5 (M) −34.5 (M) L = 2 −23.5 (I) −20.5 (M) −17.5(M) −24.5 (M) −31.5 (M) −38.5 (M) −36.5 (M) L = 3 −35.5 (I) −32.5 (M)−29.5 (M) −26.5 (M) −33.5 (M) −40.5 (M) −38.5 (M)

Moving to the next nucleotide (C) in the flow order that had a signal of0.3, the values of L=0 row are set to the highest scoring cell for eachcolumn of the previous nucleotide, in this case (A). The first columnthen is completed by adding the gap penalty beginning with the top cellvalue at L=0. Thus the highest values in each column of weighted matrixof the previous nucleotide flow are (shown in grey):

Accordingly, the first L=0 row of the next matrix is:

C = 0.3 G C T G G A L = 0 −0.5 (S0) −7.5 (D0) −14.5 (D0) −21.5 (D0)−28.5 (D0) −35.5 (D0) −34.5 (M1) L = 1 −7.5 (I) L = 2 −14.5 (I) L = 3−21.5 (I)

Moving to the next row and first column (shown as the box below), andagain using the Smith-Waterman algorithm as before:

Cell_(i-1,j-1)+score=−0.5 (diagonal cell)−4 (mismatch score)=−4.5

Cell_(i-1,j)+gap penalty=−7.5 (horizontal cell)−7 (gap penalty)=−14.5

Cell_(i,j-1)+gap penalty=−7.5 (vertical cell)−7 (gap penalty)=−14.5

Thus the value of this cell is −4.5 and has an associated M.

C = 0.3 G C T G G A L = 0  -0.5 (S0) -7.5 (D0) -14.5 (D0) -21.5 (D0)-28.5 (D0) -35.5 (D0) -34.5 (M1) L = 1  -7.5 (I)

L = 2 -14.5 (I) L = 3 -21.5 (I)

For the next entry for L=1 (shown in the box below), there is a match,so the score value would be (−7.5+5=−2.5), the vertical gap would be(−14.5−7=−21.5), and the horizontal gap would be (−4.5−7=−11.5) so(−2.5) is the maximum value as determined from the diagonally adjacentcell.

C = 0.3 G C T G G A L = 0  -0.5 (S0) -7.5 (D0) -14.5 (D0) -21.5 (D0)-28.5 (D0) -35.5 (D0) -34.5 (M1) L = 1  -7.5 (I) -4.5 (M)

L = 2 -14.5 (I) L = 3 -21.5 (I)

Continuing with the remaining cells, the completed matrix looks like:

C = 0.3 G C T G G A L = 0 −0.5 (S0) −7.5 (D0) −14.5 (D0) −21.5 (D0)−28.5 (D0) −35.5 (D0) −34.5 (M1) L = 1 −7.5 (I) −4.5 (M) −2.5 (M) −9.5(D) −16.5 (D) −23.5 (D) −30.5 (D) L = 2 −14.5 (I) −11.5 (M) .5 (M) −6.5(M) −13.5 (M) −20.5 (M) −27.5 (M) L = 3 −21.5 (I) −18.5 (M) −6.5 (I)−3.5 (M) −10.5 (M) −17.5 (M) −24.5 (M)

Again each value is weighted by how far the signal value (here C=0.3)was from the expected value (C=0) according to the weight factorWF=−abs(L-sig)*flow penalty (where the flow penalty is −5). So for L=0,WF=−abs(0−0.3)*(−5)=(−1.5) for each element in that row of the matrix.For the remaining rows: L=1, 2, and 3, the weight factors becomeWF=−3.5, −8.5 and −13.5, respectively, and the completed weighted matrixbecomes:

C = 0.3 G C T G G A L = 0 −2.0 (S0) −9.0 (D0) −16.1 (D0) −23.0 (D0)−30.0 (D0) −37.0 (D0) −36.0 (M1) L = 1 −11 (I) −8.0 (M) −6.0 (M) −13.0(D) −20.0 (D) −27.0 (D) −34.0 (D) L = 2 −23.0 (I) −20.0 (M) −8.0 (M)−15.0 (M) −22.0 (M) −29.0 (M) −36.0 (M) L = 3 −35.0 (I) −32.0 (M) −20.0(I) −17.0 (M) −24.0 (M) −31.0 (M) −38.0 (M)

Selecting the highest values (shown in grey):

Moving to the next nucleotide of the nucleotide flow order, T, with asignal of 0.2, the L=0 row and first column become:

T = 0.2 G C T G G A L = 0 −2.0 (S0) −8.0 (M1) −6.0 (M1) −13.0 (D1) −20.0(D1) −27.0 (D1) −34.0 (D1) L = 1 −9.0 (I) L = 2 −16.0 (I) L = 3 −23.0(I)

Again using the Smith-Waterman algorithm as before, the completed matrixbecomes:

T = 0.2 G C T G G A L = 0 −2.0 (S0) −8.0 (M1) −6.0 (M1) −13.0 (D1) −20.0(D1) −27.0 (D1) −34.0 (D1) L = 1 −9.0 (I) −6.0 (M) −12.0 (M) −1.0 (M)−8.0 (D) −15.0 (D) −22.0 (D) L = 2 −16.0 (I) −13.0 (M) −10.0 (M) −7.0(M) −5.0 (M) −12.0 (M) −19.0 (M) L = 3 −23.0 (I) −20.0 (M) −17.0 (M)−5.0 (M) −11.0 (M) −9.0 (M) −16.0 (M)

In this case, the weight factors for L=0, 1, 2, 3 are −1.0, −4.0, −9.0,and −14.0, respectively. Applying the weight factors, the weightedmatrix becomes:

T = 0.2 G C T G G A L = 0 −3.0 (S0) −9.0 (M1) −7.0 (M1) −14.0 (D1) −21.0(D1) −28.0 (D1) −35.0 (D1) L = 1 −13.0 (I) −10.0 (M) −16.0 (M) −5.0 (M)−12.0 (D) −19.0 (D) −26.0 (D) L = 2 −25.0 (I) −22.0 (M) −19.0 (M) −16.0(M) −14.0 (M) −21.0 (M) −28.0 (M) L = 3 −37.0 (I) −34.0 (M) −31.0 (M)−19.0 (M) −25.0 (M) −23.0 (M) −30.0 (M)

This procedure is continued for each nucleotide in the nucleotide floworder to provide the following weighted matrices:

G C T G G A G = 1.4 L = 0 −10.0 (S0) −16.0 (M0) −14.0 (M0) −12.0 (M1)−19.0 (D1) −26.0 (D1) −33.0 (D1) L = 1 −12.0 (I) 0.0 (M) −7.0 (D) −13.0(M) −2.0 (M) −9.0 (M) −16.0 (D) L = 2 −20.0 (I) −8.0 (M) −5.0 (M) −12.0(M) −9.0 (M) 2.0 (M) −5.0 (D) L = 3 −32.0 (I) −20.0 (M) −17.0 (M) −14.0(M) −12.0 (M) −9.0 (M) −7.0 (M) A = 0.3 L = 0 −11.5 (S0) −1.5 (M1) −6.5(M2) −13.5 (M0) −3.5 (M1) 0.5 (M2) −6.5 (D2) L = 1 −20.5 (I) −10.5 (I)−7.5 (M) −12.5 (M) −12.5 (I) −8.5 (I) 3.5 (M) L = 2 −32.5 (I) −22.5 (I)−19.5 (M) −16.5 (M) −21.5 (M) −20.5 (I) −8.5 (M) L = 3 −44.5 (I) −34.5(I) −31.5 (M) −28.5 (M) −25.5 (M) −30.5 (M) −20.5 (M) C = 1.2 L = 0−17.5 (S0) −7.5 (M0) −12.5 (M0) −18.5 (M1) −9.5 (M0) −5.5 (M0) −2.5 (M1)L = 1 −19.5 (I) −9.5 (I) 2.5 (M) −4.5 (D) −11.5 (I) −7.5 (I) −4.5 (I) L= 2 −29.5 (I) −19.5 (I) −7.5 (I) −4.5 (M) −11.5 (M) −17.5 (I) −14.5 (M)L = 3 −41.5 (I) −31.5 (I) −19.5 (M) −16.5 (M) −13.5 (M) −20.5 (M) −26.5(M) T = 0.8 L = 0 −21.5 (S0) −11.5 (M0) −1.5 (M1) −8.5 (D1) −13.5 (M0)−9.5 (M0) −6.5 (M0) L = 1 −25.5 (I) −15.5 (I) −5.5 (I) 6.5 (M) −0.5 (D)−7.5 (D) −10.5 (M) L = 2 −37.5 (I) −27.5 (I) −17.5 (I) −5.5 (M) −2.5 (M)−9.5 (M) −16.5 (M) L = 3 −49.5 (I) −39.5 (I) −29.5 (I) −17.5 (I) −14.5(M) −11.5 (M) −18.5 (M) G = 1.5 L = 0 −29.0 (S0) −19.0 (M0) −9.0 (M0)−1.0 (M1) −8.0 (D1) −15.0 (D1) −14.0 (M0) L = 1 −31.0 (I) −19.0 (M)−11.0 (I) −3.0 (I) 9.0 (M) 2.0 (M) −5.0 (D) L = 2 −38.0 (I) −26.0 (M)−18.0 (I) −10.0 (I) 2.0 (M) 14.0 (M) 7.0 (D) L = 3 −50.0 (I) −38.0 (M)−30.0 (I) −22.0 (I) −10.0 (M) 2.0 (M) 5.0 (M) A = 0.7 L = 0 −32.5 (S0)−22.5 (M0) −12.5 (M0) −4.5 (M0) 5.5 (M1) 10.5 (M2) 3.5 (D2) L = 1 −37.5(I) −27.5 (I) −17.5 (I) −9.5 (I) 0.50 (I) 5.5 (I) 17.5 (M) L = 2 −49.5(I) −39.5 (I) −29.0 (I) −21.50 (I) −11.5 (I) −6.5 (I) 5.5 (M) L = 3−61.5 (I) −51.5 (I) −41.5 (I) −33.50 (I) −23.5 (I) −18.5 (I) −6.5 (M)

As with the Smith-Waterman algorithm used above, to determine thealignment, a trajectory is traced back through the matrix workingcolumn-by-column and matrix-by-matrix, with the starting point being thecell with the highest value in the far right hand column of the lastmatrix. In this case, where a three-dimensional matrix is present, apath can be envisioned as being traced from one corner to the opposite,diagonal corner, for example, of a cube if all vectors were of equallength.

Here, beginning with the last matrix (corresponding to the lastnucleotide flow), the highest value in the far right hand column is 17.5(M), which is located in the L=1 row indicating that there is an Apresent. The M means that the next cell considered is the diagonallyadjacent cell, which is 10.5 (M2). Being in row L=0, there is nonucleotide present but it indicates a move to the prior nucleotidematrix, in the same column (“G”) but row L=2 because of the 2 after theM.

Now in the matrix where G=1.5, the beginning cell is in the second tolast column on the right (same column as last matrix) in row L=2, whichhas a value of 14.0 (M). Thus, being in row L=2 infers that ahomopolymer of length 2 is present for G. In other words, the alignmentsequence contains GG and currently is: G G A. The M means that the nextcell considered is the diagonally adjacent cell, which is 9.0 (M). Thiscell is in a “G” column and in L=1, thereby confirming the presence oftwo G's. The M again means that the next cell considered is thediagonally adjacent cell, which is −1.0 (M1) in row L=0. Thus, a move ismade to the prior nucleotide matrix, in the same column (“T”) but rowL=1 because of the 1 after the M.

In the matrix where T=0.8, the beginning cell is in the “T” column, L=1row, which has a value of 6.5 (M), indicating the presence of a T.Accordingly, at this point, the alignment sequence is: T G G A. The Mmeans that the next cell considered is the diagonally adjacent cell,which is −1.5 (M1) in row L=0. Thus, a move is made to the priornucleotide matrix, in the same column (“C”) but row L=1 because of the 1after the M.

In the matrix where C=1.2, the beginning cell is in the “C” column, L=1row, which has a value of 2.5 (M), indicating the presence of a C. The Mmeans that the next cell considered is the diagonally adjacent cell,which is −7.5 (M0) in row L=0. Thus, a move is made to the priornucleotide matrix, in the same column (“G”) but row L=0 because of the 0after the M.

In the matrix where A=0.3, the beginning cell is in the “G” column atthe far left, L=0 row, which has a value of −1.5 (M1). Because of thecell being in row L=0, no nucleotide is called out. However, a move ismade to the prior nucleotide matrix, in the same column (“G”) but rowL=1 because of the 1 after the M.

In the matrix where G=1.4, the beginning cell is in row L=1, which has avalue of 0.0 (M), indicating the presence of a G. The M means that thenext cell considered is the diagonally adjacent cell, which is −10.0(S0) in row L=0. Thus, a move is made to the prior nucleotide matrix, inthe same column (“starting column”) and row L=0 because of the 0 afterthe S.

In the matrix where T=0.2, the beginning cell is in row L=0, which has avalue of −3.0 (S0) so no nucleobase is called. From here, a move back tothe matrix where T=0.2, in the same column and row L=0, the cell has avalue of −3.0 (S0). Again, no base call is made. Now, a move back to thematrix where C=0.3, in the same column and row L=0, the cell has a valueof −2.0 (S0). Again, no base call is made. Finally, a move back to thematrix where A=0.1, in the same column and row L=0, the cell has a valueof −0.5 (S0) and the opposite, diagonal corner of the three-dimensionalmatrix is reached.

In sum, the alignment of the putative nucleic acid sequence (based onthe nucleotide flow order and signals from each flow) with a candidatereference nucleic acid sequence provides the sequence: G C T G G A,which accounts for the homopolymer stretch of GG in the sequence. Asseen previously with the use of the Smith-Waterman algorithm alone, sucha determination was not made.

In particular embodiments, an alignment module can receive data in SFFfile format or FASTQ file format. The alignment module can store,transmit and/or output a sample nucleic acid sequences and related dataand information in SAM or BAM file format.

FIG. 6 is a block diagram that illustrates a computer system 600, uponwhich embodiments of the present teachings can be implemented. Computersystem 600 can include a bus 602 or other communication mechanism forcommunicating information, and a processor 604 coupled with bus 602 forprocessing information. Computer system 600 can also include a memory606, which can be a random access memory (RAM) or other dynamic storagedevice, coupled to bus 602. Memory 606 can store data, such as sequenceinformation, and instructions to be executed by processor 604. Memory606 can also be used for storing temporary variables or otherintermediate information during execution of instructions to be executedby processor 604. Computer system 600 can further include a read-onlymemory (ROM) 608 or other static storage device coupled to bus 602 forstoring static information and instructions for processor 604. A storagedevice 610, such as a magnetic disk, an optical disk, a flash memory, orthe like, can be provided and coupled to bus 602 for storing informationand instructions.

Computer system 600 can be coupled by bus 602 to display 612, such as acathode ray tube (CRT) or liquid crystal display (LCD), for displayinginformation to a computer user. An input device 614, such as a keyboardincluding alphanumeric and other keys, can be coupled to bus 602 forcommunicating information and commands to processor 604. Cursor control616, such as a mouse, a trackball, a trackpad, or the like, cancommunicate direction information and command selections to processor604, such as for controlling cursor movement on display 612. The inputdevice can have at least two degrees of freedom in at least two axesthat allows the device to specify positions in a plane. Otherembodiments can include at least three degrees of freedom in at leastthree axes to allow the device to specify positions in a space. Inadditional embodiments, functions of input device 614 and cursor 616 canbe provided by a single input devices such as a touch sensitive surfaceor touch screen.

Computer system 600 can perform the present teachings. Consistent withcertain implementations of the present teachings, results are providedby computer system 600 in response processor 604 executing one or moresequences of one or more instructions contained in memory 606. Suchinstructions may be read into memory 606 from another computer-readablemedium, such as storage device 610. Execution of the sequences ofinstructions contained in memory 606 can cause processor 604 to performthe processes described herein. Alternatively, hard-wired circuitry maybe used in place of or in combination with software instructions toimplement the present teachings. Thus, implementations of the presentteachings are not limited to any specific combination of hardwarecircuitry and software.

The term “computer-readable medium” as used herein refers to any mediathat participates in providing instructions to processor 604 forexecution. Such a medium may take many forms, including but not limitedto, nonvolatile memory, volatile memory, and transmission media.Nonvolatile memory includes, for example, optical or magnetic disks,such as storage device 610. Volatile memory includes dynamic memory,such as memory 606. Transmission media includes coaxial cables, copperwire, and fiber optics, including the wires that comprise bus 602.Non-transitory computer readable medium can include nonvolatile mediaand volatile media.

Common forms of non-transitory computer readable media include, forexample, floppy disk, flexible disk, hard disk, magnetic tape, or anyother magnetic medium, a CD-ROM, any other optical medium, punch cards,paper tape, any other physical medium with patterns of holes, a RAM, aPROM, an EPROM, a FLASH-EPROM, and other memory chips or cartridge orany other tangible medium from which the computer can read.

Various forms of computer readable media may be involved in carrying oneor more sequences of one or more instructions to processor 604 forexecution. For example the instructions may initially be stored on themagnetic disk of a remote computer. The remote computer can load theinstructions into its dynamic memory and send instructions over anetwork to computer system 600. A network interface coupled to bus 602can receive the instructions and place the instructions on bus 602. Bus602 can carry the instructions to memory 606, from which processor 604can retrieve and execute the instructions. Instructions received bymemory 606 may optionally be stored on storage device 610 either beforeor after execution by processor 604.

The execution of any of the methods of nucleic acid sequencing analysisdescribed herein, where appropriate, can be carried out by anappropriately programmed computer system. In terms of hardwarearchitecture, the computer generally includes a processor, memory, andone or more input and/or output (I/O) devices (or peripherals) that arecommunicatively coupled via a local interface. The local interface canbe, for example, one or more buses or other wired or wirelessconnections, as is known in the art. The local interface can haveadditional elements, which are omitted for simplicity, such ascontrollers, buffers (caches), drivers, repeaters and receivers, toenable communications. Further, the local interface can include address,control, and/or data connections to enable appropriate communicationsamong the other computer components.

A processor is a hardware device for executing software, particularlysoftware stored in memory. The processor can be any custom made orcommercially available processor, a central processing unit (CPU), anauxiliary processor among several processors associated with thecomputer, a semiconductor based microprocessor (in the form of amicrochip or chip set), a macroprocessor, or generally any device forexecuting software instructions. Examples of suitable commerciallyavailable microprocessors include: a PA-RISC series microprocessor fromHewlett-Packard Company, an 80x86 or Pentium series microprocessor fromIntel Corporation, a PowerPC microprocessor from IBM, a Sparcmicroprocessor from Sun Microsystems, Inc., and a 68xxx seriesmicroprocessor from Motorola Corporation. A processor can also representa distributed processing architecture.

Memory can include any one or a combination of volatile memory elements(e.g., random access memory (RAM, such as DRAM, SRAM, SDRAM, etc.)) andnonvolatile memory elements (e.g., ROM, hard drive, tape, CDROM, etc.).Moreover, memory can incorporate electronic, magnetic, optical, and/orother types of storage media. Memory can have a distributed architecturewhere various components are situated remote from one another, but arestill accessed by the processor.

The software in memory can include one or more separate programs. Theseparate programs can comprise ordered listings of executableinstructions for implementing logical functions. In some embodiments,the software in memory includes a system for identifying data streams inaccordance with the present teachings and a suitable operating system(O/S). A non-exhaustive list of examples of suitable commerciallyavailable operating systems includes: (a) a Windows operating systemavailable from Microsoft Corporation; (b) a Netware operating systemavailable from Novell, Inc.; (c) a Macintosh operating system availablefrom Apple Computer, Inc.; (d) a UNIX operating system, which isavailable for purchase from many vendors, such as the Hewlett-PackardCompany, Sun Microsystems, Inc., and AT&T Corporation; (e) a LINUXoperating system, which is freeware that is readily available on theInternet; and (f) an appliance-based operating system, such as thatimplemented in handheld computers or personal digital assistants (PDAs)(e.g., PalmOS available from Palm Computing, Inc., and Windows CEavailable from Microsoft Corporation). The operating system essentiallycontrols the execution of other computer programs such as the system,and provides scheduling, input-output control, file and data management,memory management, and communication control and related services.

The system for identifying data streams can be a source program,executable program (object code), script, or any other entity comprisinga set of instructions to be performed. When a source program, theprogram can be translated via a compiler, assembler, interpreter, or thelike, which may or may not be included within the memory, so as tooperate properly in connection with the O/S. Furthermore, the system foridentifying data streams can be written as (a) an object orientedprogramming language, which has classes of data and methods, or (b) aprocedural programming language, which has routines, subroutines, and/orfunctions, for example but not limited to, C, C++, Pascal, Basic,Fortran, Cobol, Perl, Java, and Ada. In certain embodiments, the systemfor identifying data streams is written in C++. In various embodiments,the system for identifying data streams is created using Power Builder.The I/O devices can include input devices, for example, a keyboard, amouse, a scanner, a microphone, a touch screen, an interface for variousmedical devices, a bar code reader, a stylus, a laser reader, aradio-frequency device reader, and the like. Furthermore, the I/Odevices also can include output devices, for example, a printer, a barcode printer, a display, and the like. Finally, the I/O devices furthercan include devices that communicate as both inputs and outputs, forexample, a modulator/demodulator (modem; for accessing another device,system, or network), a radio frequency (RF) or other transceiver, atelephonic interface, a bridge, a router, and the like.

If the computer is a PC, workstation, PDA, or the like, the software inthe memory can include a basic input output system (BIOS). The BIOS is aset of essential software routines that initialize and test hardware atstartup, start the O/S, and support the transfer of data among thehardware devices. The BIOS is stored in ROM so that the BIOS can beexecuted when the computer is activated.

When computer is in operation, the processor is configured to executesoftware stored within memory, to communicate data to and from memory,and generally to control operations of the computer pursuant to thesoftware. The system for identifying data streams and the O/S, in wholeor in part, but typically the latter, are read by a processor, perhapsbuffered within the processor, and then executed.

When the system is implemented in software, it should be noted that thesystem can be stored on any computer readable medium for use by or inconnection with any computer-related system or method. The system foridentifying data streams can be embodied in any computer-readable mediumfor use by or in connection with an instruction execution system,apparatus or device, such as a computer-based system,processor-containing system, or other system that can fetch theinstructions from the instruction execution system, apparatus or deviceand execute the instructions.

As used herein, a “computer-readable medium” can be any means that canstore, communicate, propagate, or transport the program for use by or inconnection with the instruction execution system, apparatus, or device.For example, a “computer readable medium” can be an electronic,magnetic, optical, or other physical device or means that can contain orstore a computer program for use by or in connection with acomputer-related system or method. The computer readable medium can be,for example, an electronic, magnetic, optical, electromagnetic,infrared, or semiconductor system, apparatus, device, or propagationmedium. More specific examples of a computer-readable medium include: anelectrical connection (electronic) having one or more wires, a portablecomputer diskette (magnetic), a random access memory (RAM) (electronic),a read-only memory (ROM) (electronic), an erasable programmableread-only memory (EPROM, EEPROM, or Flash memory) (electronic), anoptical fiber (optical), and a portable compact disc read-only memory(CDROM) (optical). Note that the computer-readable medium could even bepaper or another suitable medium upon which the program is printed, asthe program can be electronically captured, via, for instance, opticalscanning of the paper or other medium, then compiled, interpreted orotherwise processed in a suitable manner, if necessary, and then storedin a computer memory.

In particular embodiments, where the system for identifying data streamsis implemented in hardware, a system for identifying data streams can beimplemented with any, or a combination of, the following technologies,which are each well known in the art: a discrete logic circuit(s) havinglogic gates for implementing logic functions upon data signals, anapplication specific integrated circuit (ASIC) having appropriatecombinational logic gates, a programmable gate array(s) (PGA), a fieldprogrammable gate array (FPGA), and the like.

Nucleic acid sequence data can be generated using various techniques,platforms or technologies, including, but not limited to: capillaryelectrophoresis, microarrays, ligation-based systems, polymerase-basedsystems, hybridization-based systems, direct or indirect nucleotideidentification systems, pyrosequencing, ion- or pH-based detectionsystems, electronic signature-based systems, etc.

Various embodiments of nucleic acid sequencing platforms, such as anucleic acid sequencer, can include components as displayed in the blockdiagram of FIG. 7. According to various embodiments, sequencinginstrument 700 can include a fluidic delivery and control unit 702, asample processing unit 704, a signal detection unit 706, and a dataacquisition, analysis and control unit 708. Various embodiments ofinstrumentation, reagents, libraries and methods used for nextgeneration sequencing are described in U.S. Patent ApplicationPublication No. 7009/0127589 and No. 7009/0026082 are incorporatedherein by reference. Various embodiments of instrument 700 can providefor automated sequencing that can be used to gather sequence informationfrom a plurality of sequences in parallel, such as substantiallysimultaneously.

In various embodiments, the fluidics delivery and control unit 702 caninclude reagent delivery system. The reagent delivery system can includea reagent reservoir for the storage of various reagents. The reagentscan include RNA-based primers, forward/reverse DNA primers,oligonucleotide mixtures for ligation sequencing, nucleotide mixturesfor sequencing-by-synthesis, optional ECC oligonucleotide mixtures,buffers, wash reagents, blocking reagent, stripping reagents, and thelike. Additionally, the reagent delivery system can include a pipettingsystem or a continuous flow system which connects the sample processingunit with the reagent reservoir.

In various embodiments, the sample processing unit 704 can include asample chamber, such as flow cell, a substrate, a micro-array, amulti-well tray, or the like. The sample processing unit 704 can includemultiple lanes, multiple channels, multiple wells, or other means ofprocessing multiple sample sets substantially simultaneously.Additionally, the sample processing unit can include multiple samplechambers to enable processing of multiple runs simultaneously. Inparticular embodiments, the system can perform signal detection on onesample chamber while substantially simultaneously processing anothersample chamber. Additionally, the sample processing unit can include anautomation system for moving or manipulating the sample chamber.

In various embodiments, the signal detection unit 706 can include animaging or detection sensor. For example, the imaging or detectionsensor can include a CCD, a CMOS, an ion or chemical sensor, such as anion sensitive layer overlying a CMOS or FET, a current or voltagedetector, or the like. The signal detection unit 706 can include anexcitation system to cause a probe, such as a fluorescent dye, to emit asignal. The excitation system can include an illumination source, suchas arc lamp, a laser, a light emitting diode (LED), or the like. Inparticular embodiments, the signal detection unit 706 can include opticsfor the transmission of light from an illumination source to the sampleor from the sample to the imaging or detection sensor. Alternatively,the signal detection unit 706 may provide for electronic or non-photonbased methods for detection and consequently not include an illuminationsource. In various embodiments, electronic-based signal detection mayoccur when a detectable signal or species is produced during asequencing reaction. For example, a signal can be produced by theinteraction of a released byproduct or moiety, such as a released ion,such as a hydrogen ion, interacting with an ion or chemical sensitivelayer. In other embodiments a detectable signal may arise as a result ofan enzymatic cascade such as used in pyrosequencing (see, for example,U.S. Patent Application Publication No. 7009/0325145, the entirety ofwhich being incorporated herein by reference) where pyrophosphate isgenerated through base incorporation by a polymerase which furtherreacts with ATP sulfurylase to generate ATP in the presence of adenosine5′ phosphosulfate wherein the ATP generated may be consumed in aluciferase mediated reaction to generate a chemiluminescent signal. Inanother example, changes in an electrical current can be detected as anucleic acid passes through a nanopore without the need for anillumination source.

In various embodiments, a data acquisition analysis and control unit 708can monitor various system parameters. The system parameters can includetemperature of various portions of instrument 700, such as sampleprocessing unit or reagent reservoirs, volumes of various reagents, thestatus of various system subcomponents, such as a manipulator, a steppermotor, a pump, or the like, or any combination thereof.

It will be appreciated by one skilled in the art that variousembodiments of instrument 700 can be used to practice variety ofsequencing methods including ligation-based methods, sequencing bysynthesis, single molecule methods, nanopore sequencing, and othersequencing techniques.

In various embodiments, the sequencing instrument 700 can determine thesequence of a nucleic acid, such as a polynucleotide or anoligonucleotide. The nucleic acid can include DNA or RNA, and can besingle stranded, such as ssDNA and RNA, or double stranded, such asdsDNA or a RNA/cDNA pair. In various embodiments, the nucleic acid caninclude or be derived from a fragment library, a mate pair library, aChIP fragment, or the like. In particular embodiments, the sequencinginstrument 700 can obtain the sequence information from a single nucleicacid molecule or from a group of substantially identical nucleic acidmolecules.

In various embodiments, sequencing instrument 700 can output nucleicacid sequencing read data in a variety of different output data filetypes/formats, including, but not limited to: *.fasta, *.csfasta,*seq.txt, *qseq.txt, *.fastq, *.sff, *prb.txt, *.sms, *srs and/or *.qv.

The present teachings encompass embodiments in other specific formswithout departing from the spirit or essential characteristics thereof.The foregoing embodiments are therefore to be considered in all respectsillustrative rather than limiting on the present teachings describedherein. Scope of the present invention is thus indicated by the appendedclaims rather than by the foregoing description, and all changes thatcome within the meaning and range of equivalency of the claims areintended to be embraced therein.

EXAMPLES

FIG. 8 is a graph comparing the sensitivity and false mapping rate(specificity) for various mapping methods. A simulated dataset isgenerated with 50 bp read lengths. The reads of the simulated datasetare mapped using various algorithms (“bwa-short”, “bwa-long”, “ssaha”,“tmap bwa short”, “tmap bwa long”, “tmap ssaha2”, and “tmap combined”).“bwa-short” is as described in Li, H, Durbin, R (2009). Fast andaccurate short read alignment with Burrows-Wheeler transform.Bioinformatics, 25, 14:1754-60. “bwa-long” is as described in Li, H,Durbin, R (2010) Fast and accurate long-read alignment withBurrows-Wheeler transform. Bioinformatics, 26, 5:589-95. “ssaha2” is asdescribed in Ning et al. (2001) SSAHA: a fast search method for largeDNA databases. Genome Res. 11, 10:1725-9.

“tmap bwa short” is the BWA short algorithm modified according tovarious embodiments of the present teaching. “tmap bwa long” is the BWAlong algorithm modified according to various embodiments of the presentteaching. “tmap ssaha2” is the SSAHA algorithm modified according tovarious embodiments of the present teaching. “tmap combined” combinesthe results of “tmap bwa short”, “tmap bwa long”, and “tmap ssaha2”according to various embodiments of the present teaching.

1. A computer implemented method of aligning nucleic acid sequenceinformation for at least one of a sample nucleic acid template against acandidate reference nucleic acid sequence, the method comprising:generating nucleic acid sequence information for the at least one samplenucleic acid template where a series of nucleotide flows to a pluralityof defined spaces provides a series of signals from the defined spaces,wherein the at least one sample nucleic acid template is discretelyassociated with the defined spaces; identifying, based on the nucleicacid sequence information, a candidate reference nucleic acid sequence;forming, for each nucleobase of the series of nucleotide flows, a matrixhaving axes and a plurality of cells, each cell corresponding to a rowand column of the axes, wherein the matrix comprises a first axiscorresponding to the nucleobases of the candidate reference nucleic acidsequence and a second axis comprising a listing of the number of lengthfrom 0 to n of nucleobases in a homopolymer of the nucleobase of thenucleotide flow; calculating a value of selected cells of the matrix inresponse to the overlap of the nucleobase of the nucleotide flow withnucleobases of the candidate reference nucleic acid sequence using alocal sequence aligning method; weighting the values of the matrix inresponse to the signal of the nucleobase of the nucleotide flow;evaluating the matrices for selected nucleobases of the series ofnucleotide flows to determine the goodness of fit; and outputting thealigned nucleic acid sequence.
 2. The method of claim 1 wherein thegoodness of fit reflects the quality of or is considered in relation tothe putative nucleic acid sequence.
 3. The method of claim 1 wherein thegoodness of fit is considered in relation to the sample nucleic acidtemplate.
 4. The method of claim 1 wherein identifying a candidatereference nucleic acid sequence comprises identifying more than onecandidate reference nucleic acid sequence and the steps of forming,calculating, weighting and tracing are performed for the additionalcandidate reference nucleic acid sequences.
 5. The method of claim 1wherein each of the series of signals is indicative of the hydrogen ionconcentration in the defined space.
 6. The method of claim 1 whereincalculating the value of each cell of the matrix comprises scoring analignment.
 7. The method of claim 6 wherein scoring an alignmentcomprises setting a match parameter value, a non-match parameter value,and a gap parameter value.
 8. The method of claim 1 wherein the localsequence aligning method is a Smith-Waterman algorithm.
 9. The method ofclaim 8 wherein the local sequence aligning method comprises determiningthe maximum of:Cell_(i-1,j-1)+a score,Cell_(i-1,j)+a first gap penalty,andCell_(i,j-1)+a second gap penalty, wherein i is the position along thefirst axis and j is the position along the second axis.
 10. The methodof claim 1 wherein weighting is performed by a function in response tothe difference between a measured signal for a nucleobase of the seriesof nucleotide flows and an estimated value of that nucleobase.
 11. Themethod of claim 1 wherein weighting is performed by a function inresponse to a homopolymer number.
 12. The method of claim 11 wherein thefunction is abs(homopolymer number−measured signal)*a penalty.
 13. Acomputer implemented method of aligning a putative nucleic acid sequenceof a sample nucleic acid template against a candidate reference nucleicacid sequence, the method comprising: forming a matrix having aplurality of cells, the cells corresponding to a row and first andsecond columns of the axes, wherein the matrix comprises: a first axiscorresponding to the nucleobases of a candidate reference nucleic acidsequence, a second axis corresponding to a listing of the number oflength from 0 to n of nucleobases in a homopolymer of the nucleobase ofthe nucleotide flow, and a third axis corresponding to the nucleobasesof a series of nucleotide flows; finding an optimal path through thecells of the matrix based on calculated values of the matrix todetermine the goodness of fit of the candidate reference nucleic acidsequence; and outputting the candidate reference nucleic acid sequence,wherein the candidate reference nucleic acid sequence is identifiedbased on a putative nucleic acid sequence and the putative nucleic acidsequence is based on a series of nucleotide flows to a plurality ofdefined spaces and a series of signals from the defined spaces.
 14. Acomputer-useable medium having computer readable instructions storedthereon for execution by a processor to perform a method comprising:generating nucleic acid sequence information for at least one samplenucleic acid template based on a series of nucleotide flows to aplurality of defined space and a series of signals from the definedspaces, wherein the at least one sample nucleic acid template isdiscretely associated with the defined space; identifying, based on thenucleic acid sequence information for the at least one sample nucleicacid template, a candidate reference nucleic acid sequence; forming, foreach nucleobase of the series of nucleotide flows, a matrix having axesand a plurality of cells, each cell corresponding to a row and column ofthe axes, wherein the matrix comprises a first axis corresponding to thenucleobases of the candidate reference nucleic acid sequence and asecond axis comprising a listing of the number of length from 0 to n ofnucleobases in a homopolymer of the nucleobase of the nucleotide flow;calculating a value of selected cells of the matrix in response to theoverlap of the nucleobase of the nucleotide flow with nucleobases of thecandidate reference nucleic acid sequence using a local sequencealigning method; weighting the values of the matrix in response to thesignal of the nucleobase of the nucleotide flow; and evaluating thematrices for selected nucleobases of the series of nucleotide flows todetermine the goodness of fit.
 15. The method of claim 14 wherein theseries of signals are indicative of the hydrogen ion concentration inthe defined space.
 16. The method of claim 14 wherein the local sequencealigning method is a Smith-Waterman algorithm.
 17. The method of claim16 wherein the local sequence aligning method comprises determining themaximum of:Cell_(i-1,j-1)+a score,Cell_(i-1,j)+a first gap penalty,andCell_(i,j-1)+a second gap penalty, wherein i is the position along thefirst axis and j is the position along the second axis.
 18. A system fornucleic acid sequence analysis, the system comprising: an aligner moduleconfigured to perform the steps of: generating a nucleic acid sequenceinformation for at least one sample nucleic acid template based on aseries of nucleotide flows to a plurality of defined space and a seriesof signals from the plurality of defined space, wherein the samplenucleic acid template is discretely associated with the defined spaces;identifying, based on the nucleic acid sequence information, a candidatereference nucleic acid sequence; forming, for selected nucleobases ofthe series of nucleotide flows, a matrix having axes and a plurality ofcells, each cell corresponding to a row and column of the axes, whereinthe matrix comprises a first axis corresponding to the nucleobases ofthe candidate reference nucleic acid sequence and a second axiscomprising a listing of the number of length from 0 to n of nucleobasesin a homopolymer of the nucleobase of the nucleotide flow; calculating avalue of selected cells of the matrix in response to the overlap of thenucleobase of the nucleotide flow with nucleobases of the candidatereference nucleic acid sequence using a local sequence aligning method;weighting the values of the matrix in response to the signal of thenucleobase of the nucleotide flow; and evaluating the matrices forselected nucleobases of the series of nucleotide flows to determine thegoodness of fit.
 19. The method of claim 18 wherein the series ofsignals are indicative of the hydrogen ion concentration in the definedspace.
 20. The method of claim 18 wherein weighting is performed by afunction in response to a homopolymer number.